This 2007 Dodge Charger SRT8 in Plum Crazy Purple is stock number 11486Z. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used sports car and Dodge Charger headquarters. This car has the 6.1 liter V8 Hemi motor, which pumps out 425 horsepower. It is a numbered car, number 141 of 300 in this color for the Charger SRT8 in 2007. It has been fully safe and inspected by our service shop. It has a fresh oil and filter change. All the fluids have been checked and topped off. And this car is 100% ready to go. If you have HD capabilities on your computer, tablet, smartphone, or television, turn them on right now because it is definitely your best way to check out the quality and condition of the car before seeing a person. And if you want to subscribe to our YouTube channel, in the lower right hand part of the screen is a gold subscribe button to see all the daily videos that we do on all of our new and used inventory. So click that and sign up. Click the bell notifications. This one comes with a 20 inch painted and polished aluminum rims. It has the Brembo brakes on it. And it has Laufen 25545 ZR20 tires. And these are brand new tires. We put those on in our safety inspection. So brand new tires all the way around. Front fender is in really nice shape. Didn't see any major dents or dings on there. Front bumper is in nice shape as well. No major scuffs or scrapes. It does have factory fog lights. Headlight lenses are crystal clear. Comes with the cowl induction hood. Looks pretty good. I didn't see any major dents or dings on that. Passender side fender is in nice shape too. Passender side rim. Pretty nice. Got one little scuff up there. On the edge there, but other than that, not too bad. As you go down this side of the car, take note of how clean the body is. How reflective and mirror-like that paint is. We take these HD videos, so if you are far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the car, you can see the car, hear the car, and have confidence in the vehicle that you're looking at before you even get here. So that when you do get here, there's absolutely no surprises and you can make a smart buying decision from the comfort of your own home. Down that side, very nice and clean. I didn't see any dents or dings. This back rim is in excellent shape. You get the Brembo brakes back here as well. And you also get these slotted rotors. Back tires are brand new too. And as we come around to the back of the vehicle, it looks really good. You get the dual rear exhaust, the satin finish spoiler. You also get the satin finish on the trunk lid there. You can see it has SRT in it. The trunk lid is in nice shape. I didn't see any dents or dings on there. And as you go down this side of the car, just as clean as that passenger side. This little disclosure of this back rim. Pretty nice condition as well. Got a couple little scuffs on there. Probably will come out. Down this side of the vehicle looks good too. Power mirrors. Inside the SRT-8 package gives you the black leather, the gray suede. You get the SRT-8 stitched headrest. Factory floor mats throughout looks like the originals. Power windows, power locks, power mirrors. Hop inside and turn the ignition on so you can see the miles and everything. This one has 55,470 miles.  Leather wrap steering wheel. Audio controls on the left. Information center controls on the right. This one comes with the touch screen radio with the factory navigation system in it. Is it also a six disc CD changer in there. Electronic stability program right there. AM FM radio. Climate controls right there. Five speed automatic transmission. Passenger side seat and format are in excellent shape as well. No rips or tears on there. And the headliner and sunroof are in really nice condition too. Up here you get map lights. Home link buttons for your garage door security systems and lane systems. And this one does have the Uconnect Bluetooth radio system in it. We'll take a quick look at the back seats. And then we'll start it up and check out under the hood and let you hear the exhaust and everything. Back seats are just as clean as the front seats. You do get the latch child safety system for any child car seats you may have to put back here. Factory floor mats back here as well. These seats do fold down for extra storage. They go down about that far. We'll also check out the trunk here. You do get child safety locks on the back doors and the bottoms of the doors and everything is really clean on this car. I believe this was a Southern car which I can verify in just a second here. Actually this one's out of Virginia but very clean. Trunk area is in nice shape as well. This one does have the tire inflator kit and that's where your battery is as well. And once again very nice and clean in the trunk. Trunk lid looks good. And we'll start it up and take a look under the hood. I was like starting it up. So I can show you there's no check engine lights or anything like that. Starts right up. I would personally like to thank you for checking out the video today. And hopefully from this HD video you will be able to tell just how clean this car is all the way around. Inside and out. Under the hood we have the 6.1 liter V8 Heming motor. Engine bay is very clean. Runs very smooth. Pulls air intake, air aid. And once again this car has been fully safety and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off. Has four brand new tires. And this car is 100% ready to go. See more pictures of this car. One of our other 450 new and used cars, trucks, SUV's, minivans, Wranglers, Challengers, Chargers, Mustangs, Camaros, Corvettes. You name it we gotta go to that website right there. www.summitauto.com. Full pictures and descriptions of every single vehicle from two locations. All at www.summitauto.com. And if you'd like to check out more HD videos. You can go to www.youtube.com slash www.summitauto.com. Remember to like, subscribe and share on this video and all the videos that you see there. In fact in a second you will see a link to subscribe to our YouTube channel in the upper left. A link to more Dodge Charger videos like this one in the upper right. A link to this video, this vehicle on our website in the lower left. And a link to one of our latest YouTube videos in the lower right. Click those check us out. And we're super excited to be offering this Ultra Clean 2007. 141 of 300 made plum crazy purple Charger SRT-8s. Thanks for checking out the video again.


Hi, I'm Eugenie and I'm a first-year M-Phil music student at Oxford University and this is a day in the life at Kiebel College. So I start off every morning in Kiebel library because I have a part-time job as the librarian assistant and it's such a beautiful space to start the day. And then I headed to the music faculty to do some violin practice for an upcoming exam that I have. Afterwards I headed over to the Kiebel Boat House with some friends to support Kiebel at the rowing and it was such a fun way to spend the afternoon and to end the day there was parents formal in the Kiebel dining hall and it's a special event where you can bring your families to enjoy a delicious three-course meal in the beautiful hall and it's the perfect way to end the day.


Hey there, iSchoolers. So welcome to week four of our iSchool Career Services podcast. This is our fourth podcast that we are broadcasting to you and we're so thrilled with the great reception we've had and hopefully- I can't believe we've made it four already. I know, four. Quick. We've got to start getting paid for these. We have to. Start charging a weekly fee. I'll have to contact my agent about that. Well, you know how much we should charge. Oh, I know. Three dollars. Three bucks. We'll be rolling in the dough. That's it. Three dollars. So, thank you, Jeff. Jeff Boutts and I, Christopher Perl are here today and we've got a really ambitious session for you guys today. Today we're gonna be talking about what to do if you do not get a summer internship for the summer that will be forever known as COVID-19 summer. And that seems to be on everybody's minds. Yeah. So especially if you're in a program and you are trying to get an internship or maybe you had one that you were looking forward to and that got rescinded or they dropped the ball on it and said, sorry, we're not taking you right now. There are ways that you can spend your summer to make sure that you're looking good for employers come next year when you're on the market for a full-time job. And so what I wanted to start off by saying is that now's the time to start thinking about a plan B, right?  There's still plenty of summer internships out there but as each day goes by, I don't wanna lie to you and I'm gonna tell you that your chances for getting a summer internship dwindle as the days go by. And so what I'd like to tell students to do is to start thinking about projects that you can work on for the summer, maybe reach out to some faculty members and start thinking about special projects that they may have. A lot of faculty members have research funds or have opportunities to take on some students during the summer, especially remotely where you can help them and that could be a resume builder for the summer. Another good idea is working on some certifications for the summer, using whether it's an official certification or using LinkedIn Learning that each Syracuse University gets for free to take on a certification or even Coursera if you're willing to take on Coursera. And some of the popular certifications that some employers are looking for, you can't go wrong with Python, Microsoft Azure was another one of them, I wrote a bunch of them down. AWS certification, Tableau for data visualization for my data analytics friends out there, Google Analytics, Splunk and any other AI certifications that can help you in the market. And the last one. Chris, I'm sorry, I was just gonna mention that there's a lot of sites now, like Coursera that you can go on, who offer certification prep for free. Yeah. So at least you can get the training for free. And then you'll have to pay for the certification, but a lot of companies are offering even the certifications for a discounted price, the actual exam itself. So it's very definitely worth looking into. That's great advice. Yeah, especially if it's remote. Like you don't have to go and actually sit in a physical classroom, you can't really do, oh, Coco's getting mad. Oh, Coco, someone's outside. And so look into that, definitely thanks for the suggestion, Jeff. And then the final thing that I would suggest, if finances are not as much of an issue for you or if you have some financial aid to take advantage of and roll in a summer class, an online class obviously, but try to select a summer class that will either help you get ahead in your program of study or one that is project-based that will allow you some great projects to work on. So that way you have something to show to the employer and to articulate during the interview, this is how I spent my summer. Yeah, I wasn't able to get an internship, just like 75% of my peers, but this is how I spent my summer. Yeah, those are fantastic ideas. Hopefully, the students will listen to those ideas that you gave and will seriously consider doing summer all of those.  So there's no reason why you shouldn't take on some of those ideas, some of those projects. I actually have three more that I wanted to add, believe it or not, to that master list that you just threw out. One of them is practicing interviewing. This is a great time to just go on, especially video interviewing. And this seems to be the type of interviewing that students struggle with the most just because they have the least experience with it. If you're a Syracuse University student, we have a tool called Interview Stream that allows you to go on and record yourself as you're answering questions, and then you can watch the recording afterwards and really get to see how you did, both facial expressions and answering the questions, how you answered them. So practicing interviewing, so that when it does come time for you to interview, you're ready to go. Something else is, and we've talked about this in the past, constantly networking, constantly seeking out information. That's all you're doing, doing informational interviews, reaching out to alumni and asking them questions about the industry that they're in and learning as much as you can about that industry.  And the last one I'm gonna mention is volunteer work. Looking for some volunteer opportunities out there, there's tons of companies, especially remote that would love to have help. It usually is for free, but you get the work on your skills and you're still helping out in the community, whether it be for an organization or even for those that just wanna help out other people that may be in times of need. So those are some other things to think about as well, that you can talk about to an employer as to what you did during this time of, we'll just call it downtime for right now, because we know eventually it's going to get better. Yeah, yeah, no, I really, those are awesome three practical ways, strategies, especially the interviewing piece for international students who typically struggle with sort of the unusual interview occasion and then you have to do it on video is also very stressful. If you've got the time, now's the time to devote to that. Absolutely, absolutely agree. I think that getting a new certification, throwing on practice interviewing and maybe using that new skill that you got in that certification and a volunteering type activity to really hone that skill that you just got. Man, how can you go wrong with that? You can't go wrong with that formula. Yeah, nice. That works. Yeah, and look, we're not saying don't enjoy yourself this summer, right?  But for a nice chunk of your week, try to do something productive so that way you're not wasting away your summer when you alternatively could have had a summer internship. Well, and not only that, it helps so that you're not feeling sorry for yourself and you're not just sitting there and you're thinking about what could have been.  That's the idea. Amen. Yeah. Yeah. Wow, people must think I'm very religious because on this podcast, I'm always saying amen. Amen. Amen. Hallelujah. You say amen a lot. Amen. I'm just glad to see that you changed your shirt. I did blue today. Yeah, I like it. Normally I do, I have my olive green, I have my hoodie, my gray hoodie and I got today my blue one. Yeah, there's no cat hair, no stains. Not yet. Yeah, it's good. Next week, hopefully I will have that in a different one. Ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, jokester Jeff. Yes. So anything else, Jeff, that you'd like to tell our students this week before we sign off with week four podcast? Well, the only other thing I would say is like you had mentioned at the beginning of this podcast, please don't use this as an excuse for stopping to look for internships. That is not the point of this podcast. The point is in the meantime, while you're searching for that opportunity for you to get an internship, these are things that you can do to help you fill that void. Yeah. Good work. Yeah. Nice, Jeff. Good topic. Yeah, good, very good topic. So students send us your questions so we can help answer for week five for next week. Yeah. You got it. Have a good week, everyone. Be safe, be healthy. Hey, you too. Thanks for your help today, Jeff.


After delving into a bit of pure mathematics in the last few lectures, I want to look at what all this has to do with the Fourier transform. So what tools do we have in our arsenal? We have sine waves and cosine waves. We've learned about how we can shift a signal space by adding sine and cosine waves together. And we've found a new shorthand way of doing mathematical operations with sines and cosines by using the three forms of a complex number. We're now going to use all of these tools as we look at the secret of how the Fourier transform actually works. This secret is called convolution. But before we start to talk about convolution, let's first remind ourselves of what Fourier said about signals, or as he called them, functions. Any function of a variable, whether continuous or discontinuous, can be expanded in a series of sines of multiples of the variable. So in other words, Fourier saw any signal as a lot of sine waves, each with its own frequency, phase and amplitude, all added together. This is what a transform is, a way of building up a signal out of simpler building blocks. In Fourier's case, he built his signals out of sine waves, but Fourier was by no means the only person to invent a transform. There are many other types of transforms. The Laplace transform, for example, overcomes a big disadvantage of the Fourier transform. One problem with the Fourier transform, which we'll look at later on, is that it assumes that signals repeat themselves forever, which clearly many of them don't. This is where a Laplace transform has a distinct advantage. Whereas Fourier assumes that signals are made up of a collection of sine waves with a constant amplitude, Laplace constructs his signals from a collection of decaying sine waves, which decay to nothing, or near enough, long before forever is reached. Another type of transform is the wavelet transform. A wavelet is a little burst of sine wave, which starts at zero amplitude, grows to some value, then decays back to zero again. By adding lots of wavelets together, changing the point in time at which each wavelet starts, the shape of its envelope and its frequency, you can make up any signal you like, just as you can with Fourier's sine waves. So Fourier, building his signals as he did out of sine waves, claims that he could take any signal, break it down into its constituent waves, and tell us what the properties of each wave were. We discovered back at the beginning of the course that a sine wave has three properties, frequency, amplitude, and phase. So at the end of Fourier's transform, we expect to end up with a list of waves containing three columns for each wave, one for frequency, one for amplitude, and one for phase. So what is convolution? Convolution is the mathematical equivalent of looking for your slippers. I have no idea where I put my slippers, so I have to search in every room. I know what they look like, so I'll recognise them when I see them. What happens if I find my wife's slippers first? Well, I know they're not mine because my wife's slippers are grey and mine are purple. Here are my slippers! I wonder how they got there. Applying this analogy to the world of signals, my slippers are like the sine wave that we're looking for within our signal. I'll know when I find it, as I know what frequency I'm looking for, but I don't know where or other when it occurs in the signal. In other words, I have no idea what its phase is, so just as I have to search every room in my house for my slippers, I have to search every phase in my signal for the sine wave that I'm looking for. To demonstrate how convolution works, let's look at a more visual example. By this point in the course, you probably know what I look like. Here I am. Now, imagine that I was in the middle of a crowd of people. How would you find me? Well, one way you could do it would be to compare each person in the crowd with the image of me that you have in your memory. Let's call this the test image. If we slide the test image over all the people in the crowd, the moment the test image and the real me converge, you'll know that you have found me. To find the phase of the sine wave with the frequency we are looking for in our signal, we do exactly the same thing. We slide or convolve a cosine wave of the same frequency over the signal. Let's call this cosine wave the test wave. Now, why am I using a cosine wave and not a sine wave? Well, it's simply a matter of convention. As far as the maths is concerned, I could use either. After all, sine waves and cosine waves are the same wave, just with a 90 degree phase difference between them. However, very soon you're going to understand the Fourier transform formula. And that formula is written in the language of complex numbers. Therefore, I want to keep things consistent. When writing a complex number, we always start with the real part, which corresponds to the cosine component. So just as complex numbers begin with the cosine component, so will I. So here's our test wave, a cosine wave, and I'm slowly going to slide it over my signal by increasing its phase. The moment the test wave converges with the sine wave we are looking for, we know that we have found the phase of the sine wave within our signal. Now, involving the two waves in this manner is all very well for us humans. We can easily identify by sight when the two waves converge. But how could we detect the point of convergence mathematically? How would a computer do it? What we need is to somehow generate a number, a score that indicates how well the two signals match. When they don't match at all, the score needs to be low. When they match completely, the score needs to be high. Well, one way we could do this would be as follows. Let's reset our signal to its initial position. Now, I'm going to multiply each point on our test wave with each point on the signal and plot the multiplied signal on a new graph. At an angle of 0 degrees, our test wave has a value of 1 and our signal has a value of 0.17. So we multiply these two points together which gives us 0.17 and we plot that new point here. At an angle of 2 degrees, our test wave has a value of 0.98 and our signal has a value of 0.34. So we multiply those two points together which gives us 0.34 and we plot that point here. At an angle of 4 degrees, our test wave has a value of 0.94 and our signal has a value of 0.5. So we multiply those two points together giving us 0.47 and we plot that point here. We do this for all the points which gives us a new multiplied signal shown here in green. We then measure the area enclosed by the multiplied graph. This gives us a single value which is the score of how well matched the test wave and the sine wave which I'm looking for within my signal are. The score for this initial position of the test wave is 31. Now let's increase the phase a little and do the whole operation again. Each point on the test wave is multiplied by each point on the signal and the resulting area enclosed by the graph gives us the score of how well matched the signal and test wave are. If I animate the process, look at what happens to the score. As the waves move closer and closer to being in phase with each other the area enclosed by the multiplied graph increases meaning that the score increases too. When the two waves are in phase, the score reaches its highest value 180 in the case of these two waves then begins to fall off again as the two waves slip out of phase. When the two waves are at their most out of phase the score is at its lowest value minus 180 in the case of these two waves. So when my test wave reaches a phase of 80 degrees the two signals match perfectly and the score is at its highest value. I have found the phase of the sine wave in my signal. That's all very well for a simple signal like this but what about a more complicated signal? What about a signal made up of more than one sine wave? Which sine waves are present in this signal? What are their frequencies? What are their phases? And what are their amplitudes? Well just like the slippers, we have to look for them. Let's start by convolving a test wave with a frequency of one and an amplitude of one over our signal. When we multiply all the points on our test wave by all the points on our signal and plot them on the multiplied graph it doesn't matter what the phase is there is always as much of the green line above the x-axis as there is below it. This means that when we calculate the total area enclosed by the graph we'll always get a score of zero. This indicates that our signal does not contain a sine wave with a frequency of one. Let's try convolving a test wave with a frequency of two over our signal. This time as we increase the phase we can see how the multiplied signal shifts up and down over the x-axis. When we measure the area enclosed by the multiplied graph we see that the score is not zero. So our signal does contain a sine wave with a frequency of two in it. Finding the point at which the score is at its greatest tells us that the phase of this sine wave is 30 degrees. Let's try convolving a test wave with a frequency of three over our signal. Again the multiplied signal shifts up and down over the x-axis. So our signal does contain a sine wave with a frequency of three in it. The score is at its highest point at 60 degrees. So the phase of this sine wave within our signal is 60 degrees and so on. If I were to try a test frequency of four on this wave I would get zero again as this signal does not contain a sine wave with a frequency of four. So whenever we try a frequency that does not exist in the signal we get a value of zero in the score no matter what the phase. And when a frequency does exist in the signal we get a score that is non-zero. The moment we find the point at which the score is at its maximum we have found the phase of the sine wave we are looking for. While we've been searching our signal for sine waves we've found their frequencies and their phases and we haven't said anything about their amplitudes. Well that's just what the score is. The maximum score we found for each frequency is proportional to the amplitude of the sine wave we are looking for. It doesn't actually tell us what the original amplitude was but it does tell us what its relative contribution is to the overall signal. Just for curiosity's sake what will we have to do to make the score equal to the actual contribution of this particular sine wave in the original signal? Well we'd have to divide the score by a half of the period of the signal. The period of this signal is 360 degrees so a half of the period will be 180 degrees. For this test wave with a frequency of three the maximum score was 72. So if we divide 72 by 180 we get 0.4 which is the actual amplitude of this frequency within the signal. However as we're only concerned with splitting the signal apart into its constituent sine waves the relative contribution or as I called it the score is good enough for now. So our signal is made up of two waves the first has a frequency of two at a phase of 30 degrees and a relative amplitude of 90 the second has a frequency of three at a phase of 60 degrees and a relative amplitude of 72. When these two waves are added together we get a result which looks like our signal. So using convolution we've managed to deconstruct our signal into its constituent sine waves we have just found our first Fourier series. Now Fourier was a wildly old mathematician although we knew he could get his answer using convolution he could see how hard it had to work to get there Fourier noticed there was a slightly quicker way of doing it What I'm about to show you is not the fast Fourier transform we'll take a look at that in a later lecture What I want to demonstrate here is how we don't actually need to do the whole convolution operation i.e. slide our test wave all the way over our signal to get our result We just saw how the score increases to a maximum the nearer the test wave and the sine wave we're looking for in our signal are to being in phase with each other If I trace the line which the score value describes as we convolve the two waves just look at which function that line makes It's a phase shifted sine wave with the same phase as the sine wave we are looking for within our signal But we know that any phase shifted sine wave can be described by adding a non phase shifted cosine wave and a non phase shifted sine wave at the same frequency but different amplitudes So instead of having to perform the entire convolution all we need to do is multiply our signal firstly by a cosine wave and then by a sine wave then use Pythagoras and the inverse tangent mode to calculate the amplitude and phase shift from the two scores for each wave So let's do just that for our signal The first frequency that was present in our signal was 2 So let's start with that frequency If I calculate the score using a non phase shifted cosine wave as my test wave I get 78 If I calculate the score using a non phase shifted sine wave as my test frequency I get 45 Using Pythagoras the square root of 78 squared plus 45 squared equals 90 Using the inverse tangent rule inverse tan of 45 divided by 78 equals 30 degrees the same answer as before The second frequency present in my signal was 3 So let's calculate for that frequency If I calculate the score using a non phase shifted cosine wave as my test wave I get 36 If I calculate the score using a non phase shifted sine wave as my test wave I get 62 The square root of 36 squared plus 62 squared equals 72 Using the inverse tangent rule inverse tan of 62 divided by 36 equals 60 degrees again the same answer as before So let's review what we just did Firstly we multiplied every point of our signal by every point on a cosine wave at a known frequency take as a multiplied cosine signal which we plotted on a new graph We then found the area enclosed by that graph which we used as a score or a relative amplitude for the cosine component at that frequency We then multiplied every point of our signal by every point on a sine wave at the same frequency as the cosine wave to get a multiplied sine signal which we plotted on a new graph We then found the area under that graph which we used as a score or relative amplitude for the sine components of that frequency We then repeated the whole process again and again at many different frequencies until we had found all the frequencies within our signal So how can we express what we've just done in a mathematical language? Well, we start with a signal I said at the beginning of the course that I would demonstrate how Fourier worked by using sound signals Sound is a signal whose amplitude changes over time So let's call our signal x of t The t denoting that the variable in our signal is time First of all, in stage one we multiply the signal by a cosine wave But the x axis of a cosine wave is usually an angle Back in the lecture on phase we saw how we could scale our x axis to fit the 360 degrees of a circle by multiplying our time value by the frequency we are looking for and then multiplying the result by 360 degrees Well, that's all very well if we were working in degrees like we have been until now However, remember that when your calculator calculates the cosine or sine of a value using the infinite series we saw in the lecture on Euler's identity it is actually working in radians So we have to convert the time value not into degrees but into radians Instead of there being 360 degrees in a circle we say there are 2 pi radians in a circle So we multiply our time value t by the frequency f we are looking for and then by 2 pi radians So in stage one we multiply our signal x of t by the cosine of 2 pi f t Here is what I get when I multiply the sound signal coming from the violin we passed on the way to the cosine wave Now we need to find the area under the graph of our multiplied signal to obtain the score which represents the amplitude of the contribution of this cosine wave to the overall signal But how do we do that? If we wanted to calculate the area of a rectangle we would take the height of the rectangle and multiply it by its width But our signal is not a rectangle Is there any way to make it into one? Well we could make it into lots of rectangles or rather we could break it down into lots of slices and treat each slice as if it were a rectangle and then add the areas of all the rectangles together You can see how the blocky rectangles do approximate the shape of the multiplied signal If we reduce the width of each rectangle and increase the number of rectangles then we get a better approximation The thinner the rectangles and the more of them there are the closer we get to the actual value of the area under the graph If we were to make each rectangle infinitely thin and increase the number of rectangles to infinity we could calculate the area exactly This is known as integration which we represent mathematically by an integration sign So to find the area under the multiplied cosine graph we take the integral of our multiplied signal x of t times cosine 2 pi f of t with respect to t i.e. each slice is t seconds thick where the difference between one t and the next t is infinitely small We write this mathematically as the integral of x of t times cosine 2 pi f of t dt But an integral has to have limits t has to start somewhere and end somewhere Well, in a repeating signal such as the one we have here it's enough to look at one cycle of the signal as after that cycle is complete the signal will just repeat itself In our signal here you can see that everything repeats itself every 3.5 milliseconds So we say that the period of the signal is 3.5 milliseconds and we integrate it between time equals 0 and time equals 3.5 milliseconds Now as this is a repeating signal it doesn't actually matter where we set our limits so long as we integrate over exactly one cycle Imagine this signal went on forever Imagine it didn't have a beginning or an end just as the signal will repeat itself again and again and again into the future so it has already repeated itself again and again since the ancient past So just as our graph here looks from now when time is 0 into the future we could also look back into the past when time was less than 0 and the signal would still look the same Instead of integrating from 0 to 3.5 milliseconds we could integrate from minus 1.75 milliseconds to 1.75 milliseconds and the result of the integral will still come out the same so long as the period over which we integrated remained exactly 3.5 milliseconds which is the period of this particular signal Now, not all signals have a period of 3.5 milliseconds How do we write the limits of the integration for an arbitrary signal with a period of p seconds? Well, if we always ensure that our time equals 0 point is exactly at the centre of the graph then we need to integrate from a point in time that is minus 1.5 of the period until a point in time which is plus 1.5 of the period so our integration limits become minus p over 2 and plus p over 2 But why is that important? Why not just integrate from 0 to the period p like we did before? What's all this dividing the period by 2 business? We'll answer that question towards the end of the lecture So now we have the score for how much the cosine wave at this first frequency contributes to our overall signal The next stage is to repeat all the steps we just took only this time using a sine wave at the same frequency We take our signal multiply it by a sine wave and then integrate to find the area under the graph giving us the score which represents the amplitude of the contribution of the sine wave to the overall signal So now we have two separate integrals which I'm going to call and the sine integral But having to deal with two separate equations is rather messy Is there any way we could combine them into one integral? Could we, for example, add the two integrals together? Well, unfortunately, no That will give us a result that is simply the sum of the areas under both graphs which would give us the wrong answer Remember, in order to work out the phase of the particular sine wave we are looking for or, in other words, when exactly it occurs in our signal we have to keep the scores for the cosine and sine components separate But how can we do that and still combine our two integrals into one equation? Well, in the last few lectures we've been talking about a special number that does just that The imaginary number i If we multiply one of the integrals by i we could have our cake and eat it, so to speak But which integral? Well, the integral with the sine in it of course, just like Euler's formula multiplies the sine term by i So now, if we multiply the sine integral by i we could add the two integrals together or even take one away from the other, and it wouldn't make any difference to the result as the i would keep them separate So, what should we do? Add or take away? Well, the answer is actually more political and mathematical political in the sense that whereas mathematically it doesn't really matter which sine we use everyone has to agree to do the same thing to avoid confusion In this course we're learning about the Fourier transform which is a method of breaking down signals into their constituent sine waves It sounds to reason therefore that if Fourier knows how to break signals down he can also take those sine waves and put them back together again to recover the signal, and indeed he can, using the inverse Fourier transform We don't have time in this course to look in any detail at the inverse Fourier transform, but I will just say that the equations for the Fourier and inverse Fourier transforms look quite similar So, to differentiate between them the convention has grown up we denote the Fourier transform with a minus sign and the inverse Fourier transform with a plus sign between the integrals So, not wanting to flat convention let's combine these two integrals together by putting a minus sign between them Mathematicians like to be tidy If they can they like to reduce their equations to be as short as possible For example do we really need the two integration signs? After all as we saw integration is simply adding an infinite number of rectangular areas together Each of these integrals simply gives us a number So, for the sake of the following example let's do away with all the signs and cosines a second and deal with some simple numbers Imagine I wanted to do the following calculation 9 plus 11 minus 2 plus 3 9 plus 11 is 20 and 2 plus 3 is 5 So, 20 minus 5 equals 15 However we could remove the brackets making sure of course we can change the sign in the second set of brackets as this is a minus operation and do the whole calculation at once without having to calculate each bracket separately 9 plus 11 equals 20 minus 2 equals 18 minus 3 equals 15 This would appear to indicate that just as I can combine the calculation of two brackets into one calculation so I can combine the two integrations into one and we would get the same answer If this is true of two integrals which we actually do want to add together how much more so is it true of two integrals that we're not really adding together at all because the I will keep the sign term separate anyway So we can combine the cosine and sign integrations into one big operation but we can go further Our signal x of t is multiplied by the sign term and by the cosine term So, we could take x of t out as a common factor and put everything else in brackets But hey, look at this inside the brackets it's Euler's formula with a few minor differences The theta in our case is 2 pi f t and instead of adding the cosine and sign terms together we are subtracting them instead So, we can replace the entire brackets with E to the minus I 2 pi f t The minus sign is there because we have the cosine term minus the sign term So, this gives us a little equation which describes how we calculate the contribution of the cosine and sign terms at our first test frequency Now, we need to run this equation again and again at many different frequencies or in other words, we need to keep changing the value of f We write this like this n is an index When n equals 1 we are testing our signal with our first test frequency f1 and this gives us a result c1 c1 is a complex number whose real part tells us the score of the contribution of the cosine wave at frequency 1 and whose imaginary part tells us the score of the contribution of the sine wave of frequency 1 When n equals 2 we are testing our signal with our second test frequency f2 This gives us a result c2 c2 is also a complex number whose real part tells us the contribution of the cosine wave at frequency 2 and whose imaginary part tells us the contribution of the sine wave at frequency 2 and so it is for c2, c3, c4 and so on We generalize this by calling the terms by the collective name cn So that's it There you have it That's how the Fourier transform works and what the equation means Job done End of course Well Not quite What we just calculated is not the Fourier transform It's a Fourier series What's the difference? Remember Fourier's claim that any function could be expanded in a series of signs and multiples of the variable? Well this claim was a hotly debated subject at the time As we learned in the introduction to the course eminent mathematicians like Lagrange and Laplace both challenged Fourier's paper on the subject and it seems with good reason It took the further work of Peter Gustave Lejeune de Richelais to give a satisfactory demonstration of Fourier's claim However, there were certain restrictive conditions that had to exist for Fourier's idea as he'd proposed it in his paper to work The problem with Fourier's claim is indicated by the limits of the integral Remember that we found the area under the graph of the multiplied signal over one cycle of the signal from time equals zero to the period of the signal or as we wrote it before from minus a half of the period to plus a half of the period Only repeating signals have a cycle The whole meaning of the word cycle is something that goes around and around again and again in other words, a signal that keeps repeating itself The problem is, repeating signals are not the only signals out there In fact, most of the useful signals we encounter from day to day don't repeat themselves The words that I'm saying to you now are a kind of signal a sound signal If I was to repeat the same sentence to you over and over and over again in this lecture, you'd very quickly get bored and most likely switch off as no new information can be imparted in a repeating signal Hence, Fourier's claim that any signal can be expanded in a series of signs cannot be true Only repeating signals can be expanded in a series of signs But here we are spending all this time learning about a mathematical idea that is so revolutionary it underpins most of the electronic communication we have nowadays not to mention many other applications that Fourier couldn't even have dreamed of If the Fourier series only allows us to model a small proportion of signals how comes it so useful? Well that was thanks to the Richling who made some small but significant changes to Fourier's equation What happens, he asked if the signal doesn't repeat itself If a signal doesn't repeat itself then it cannot have a period or can it The word never suggests infinity Maybe we could say that the signal actually does repeat itself but it will only repeat itself after an infinite amount of time Therefore the limits of the integral must expand to encompass the whole of time from minus infinity to plus infinity or to put it another way the signal has never repeated itself and the signal will never repeat itself again This is why I changed the limits of the Fourier series equation before from looking at the signal from time equals zero to the period to looking at the signal from minus half of the period to plus a half of the period I wanted to give the integral consistent with the way we write the Fourier transform equation looking in both directions into the past and into the future of the signal But now we have a problem and that problem is called infinity How can we calculate the infinite? As we'll see it's not only the period but the non-repeating seal that is going to become infinite but also the length of the list of sine waves that we need to describe it Come with me as we journey into the infinite and we discover how Delichlet turned the Fourier series into the Fourier transform For more on how the Fourier transform works online course head over to works.com slash full dash course


Hello everyone, welcome to Options with Doug, streaming live daily on Bookmap Discord and the Bookmap YouTube channel at 1.30pm Eastern Time. Before I get started, I need to go through the general disclosure. All bookmap limited materials, information, and presentations are for educational purposes only and should not be considered specific investment advice nor recommendations. Risk disclosure, trading futures, equities and options, involves substantial risk of loss and is not suitable for all investors. Past performance is not necessarily indicative of future results. The focus of my presentation and the focus of the options-dog chat channel in Discord is options, order flow, the impact of options markets on stocks and futures, and the influence of market maker hedging flow on price action. I have a two-step process for trading and the first is planning and I use positional analysis. I look at how traders and market makers are positioned in the options market and how those positions change from day to day to develop a thesis regarding the expected volatility and trading range for the day. And the second step of my process is execution. And I look at real-time order flow in Bookmap and real-time market maker hedging flow in Spot Gama Hero to confirm my thesis and to help develop a directional bias as well as for setups. And just to be clear, when I talk about setups, I'm going to be talking about an underlying asset, whether it's the S&P 500 or a stock like Apple or Tesla. I'll be talking about the underlying and the setups can be taken any number of ways with shares, with futures, or options, single options or option spreads up to you. I'm just talking about an analysis based on the options market and then talking about setups and underlying assets that can be taken, again, any number of ways. And questions and comments are welcome and I will be watching the option stash dug chat channel and discord and also the chat and YouTube for your questions and comments. So please feel free to post your questions and comments. All right, let's get started. What I want to cover today, first of all, go over news events, economic data and events for the week. I'll talk about my positional analysis and then talk about some setups. All right, so first of all, economic data for the week. There's a lot of pretty much minor data that came out that comes out this week today. I think there was some housing data at 10 a.m., something at 10 a.m. and then starting tomorrow. The only thing that's marked here with high significance is the building permits tomorrow at 8 30 a.m. Eastern time and then for the rest of the week just minor medium or low impact data, jobless claims, manufacturing index, PMI data on Friday, and also Friday note is the monthly expiration. So that is the March 21st, April 21st monthly expiration. All right, let's talk about positional analysis now and I'm going to go look at book map and this is showing key levels as well as order flow again in book map for the S&P 500 futures. Normally I show a couple of thinkorswim charts, a larger time frame, but for some reason SpotGamma did not update the thinkorswim script for today so the levels are out of date on my thinkorswim chart so I'm not going to show that and the S&P 500 ES is trading in a narrow range today as you can see and let's just zoom a little bit. Here are some levels shown on my chart for the again ES S&P 500. I have two columns of notes here and the first is the SpotGamma cloud notes provided to SpotGamma subscribers for a variety of platforms and these appear to be up to date and this is showing first of all key SpotGamma levels at SPX so this is SPX 4150 and converted to an equivalent ES number. Looks like SpotGamma is using a 27 point difference and I'm using a 25.25 point difference between ES and SPX. Alright so in YouTube Eli asks is a think script you use something you share uh no it's not that is something that's provided to um SpotGamma subscribers and they provide these levels again for a variety of platforms and I'm showing the levels in book map and again for some reason the think script was not uh was not updated today it was showing levels from last week so I did not uh I'm not showing that today and then also here's the volatility trigger and that is again for SPX I'm showing it just a little bit lower so I'm showing my cloud notes here and here I have the 4150 level I'm also showing key SPI levels and there's the SPI 413 volatility trigger and you can see that that acted as resistance today this morning between 9 30 and 10 30 so the for uh for the first hour this morning that acted as resistance and note this is also um I'm also showing ES numbers and this is the I show the 50s and the zeros for ES and so that's the ES 4150 level and Eli asks another question and Eli asks does the price lines add on allow you to set auto updating formulas I don't know I don't think so I have never looked into that um I'll show you what I do uh and just a minute and I don't think the uh the levels change like the ES SPX difference I don't think it changes enough during the day to make a difference and I really don't want to see those levels jumping around I want something stable so I change that every day and I have um thanks to another thing script that I will share in discord some a member in discord shared a thanks script and I modified it made a couple of others that calculate both the the ES SPX difference and the ratio of SPX to spy and the ratio of ES to spy and I'll show that in just a minute so here is the um again back to the ES futures S&P 500 futures this is as Eli asked this is my I'm using the price lines add on here for these so I fill out these numbers in a a spreadsheet my own spreadsheet this morning and those levels then are shown in this column and it also draws the lines and I like the lines it makes it very easy to see as you're trading um these levels again the spy volatility trigger at 413 acting as resistance and the ES 4150 acting as support and I'll talk more about setups uh in a few minutes all right let's while I'm mentioning that thanks script let's just take a look at that and I have these on uh this is a thinkorswim chart and this is showing spy and what I'm the scripts that I have are shown in these badges here so here is the and I will share these in discord right so first of all here is the ES minus SPX and right now it appears to be varying between 25 and 25.5 so I just took 25.25 looks like it's spending more time at 25 and then here is the ES spy ratio at about 10.0904 is what I use today and that has uh not changed much so I think an auto update I'm not sure would would be that helpful I just I set these levels uh ES minus SPX I start using the the prior day this ES divided by spy that's shown when spy starts trading and then here is SPX divided by spy that's the SPX spy ratio and I use that for showing the SPX levels on my spy chart and then this ES spy ratio I use that for showing the spy levels on my ES chart so let's go back so this is so I calculate the rate or I I get the ratio from that think script for the spy levels and I just use that number and calculate there the difference or the ratio and I use that number in my spreadsheet all right so that is the SP500 the levels that are in play very narrow range today let's talk about shifts in levels now and there were a few for SPX the volatility trigger shifted higher from 4095 last Friday to 4110 today and also the spy SPX I'm sorry SPX put wall shifted higher from 3800 to 3900 and then for spy the volatility trigger shifted higher from 411 to 413 and then for QQQ the volatility trigger shifted higher from 316 to 318 and the put wall also shifted higher from 300 to 315 all right let's take a look at gamma levels now the absolute gamma levels and we'll see where those levels come from let's go all right so these are the levels this is SPX we'll start there this is showing the absolute gamma levels and this will all right a batch I'm not sure I understand your question I haven't talked about any setups yet or I haven't talked about hero so I'm not sure I understand your question you may be jumping ahead all right so here's the the gamma levels and maybe you could clarify maybe you're I'm not again I'm not sure I understand your question in this in this context so anyway here's the SPX the absolute gamma levels and this is showing positive gamma or call gamma above in the orange lines this is market makers position and negative gamma or put gamma with the blue bars all right so here is the 4000 level that is the absolute gamma strike the strike with the largest absolute gamma that can be act as support resistance or a magnet for price and here's the 3,900 put wall that's the strike with the largest net negative gamma and that is expected to act as support and then here's the 4,200 call wall the strike with the largest net positive gamma and that can be expected to act as resistance and again the for SPX volatility trigger is at 4,110 and that is spot gamma's proprietary gamma flip level below that level market makers position on the gamma curve is negative and that means they have to trade with price to hedge their delta exposure and that tends to increase volatility that's typical of a negative gamma environment and above that level market makers position on the gamma curve is positive and they have to trade against price to hedge their delta exposure and that tends to reduce volatility in a positive gamma environment so that is SPX those are the key daily levels that i track let's take a look at spy now i'm going to zoom in on this chart and again positive gamma shown above with the orange bars positive gamma or called gamma and blue bars are showing negative gamma or put gamma and here's the 4,10 here's the 4,10 key gamma strike or absolute gamma strike for spry for spy strike with the largest absolute gamma and here is the 400 put wall strike with the largest net negative gamma can be expected to act as support and then the call wall at 4,15 strike with the largest net positive gamma and there's the 4,13 volatility trigger for spy so we i ask where can i you're logged into discord where you can find the chat room the chat room go to so it's in book map and look for weekly live webinars and then the options dash dug chat channel and then i'm also streaming in discord in the options with dug channel and i will post the think scripts after this webinar today i have not posted those yet so i'll post those later and those are the ones that calculate the espx difference and the espi ratio and the espx spy ratio all right so those are the levels for spy and normally i have to do a refresh before looking at qqq and for the nasdaq i just look at qqq and here is the 315 put wall support level the 320 is the call wall and the key gamma strike or absolute gamma strike so those are the levels that are in play for qqq all right let's take a look at one other chart here well just to point out again friday is expiration and note this is delta notional note that this the orange dominates the orange is larger than the uh than the blue delta notional so this is a call dominated expiration right here's the vana model this is for espx this is showing this chart is showing two curves the first this light gray shows how market makers delta notional changes with changes in price and that's all the light gray curve is showing and Gabe says hey Doug seems like the discord link is invalid uh i'm not sure uh exactly what you're referring to if you don't belong to discord yet if you have not signed up and it's free for everyone whether you're a book map subscriber or not there should be a link on the uh on the book map website and if you're having trouble with that just contact uh book map support support at book map dot com all right so this is the vana model for spx and this light gray curve is showing how market makers delta notional changes with changes in price and that's all the light gray curve is showing and what this is showing is as price increases market makers delta notional increases and they have to sell futures to hedge their delta exposure and that is typical in a positive gamma environment and then this kind of pink purple curve is adding implied volatility to that so that is showing how market makers delta notional changes with changes in price and implied volatility and that's the vana effect and that is that vana is the change in delta with a change in implied volatility so what this is showing is as price increases there's not much of a a vana tailwind this pink curve is really not a lot not a lot different on the upside here than the the delta only the light gray curve and then on the other hand as price falls as price decreases and implied implied volatility increases then this is showing that market makers delta notional will change will increase and they'll have to sell futures to hedge their delta exposure as price drops and that's typical in a negative gamma environment all right let's that's for spx let's just take a quick look at spy and we're just looking at this curve right here pretty similar and then also qqq all right Gabe thanks for the thanks for the kind words glad you're enjoying it all right so that's vana model now let's take a look take a quick look at some data here and just to point out gamma notional this is market makers position on the gamma curve for spx spy ndx and qqq all these numbers are positive again market makers position on the gamma curve is positive that means that traders are short calls for an index market makers a long call since the positive gamma position and they have to sell futures as price rises to hedge their delta exposure and then when price drops they can buy back those futures and that again tends to subdue volatility in a positive gamma environment so given that my thesis for the day and my plan for the day was definitely looking for a trading range today not a not a trend day but a a range day all right let's take a look at some setups now and i want to talk about the s and p 500 first i'm just going to point out so this is the s and p 500 it's a combined signal for spx spy xsp which is not significant and also now new starting last week es futures okay so this is a combined signal for all these instruments and i typically look at this signal or spx so spx seems to um either again spx or the total combined signal seems to be providing the best most tradable signal so that's spx that's one component of this s and p 500 combined signal and let's take a look at spy and i have not gotten that much out of the spy signal recently it seems to be that spx is um having a stronger influence on on price action and order flow and then we can also look at just the future signal here and that's the signal and that's definitely bearish today so there are a number of ways to slice and dice this and then each um for each signal we can look at total expirations or just zero dte and we can also look at puts and calls separately so let's go to the spx signal here and i'm going to first of all zoom in on the morning session and this provided a couple of great short divergent setups and the first was at 10 am notice price rises hero levels off then starts to fall and price moves up setting up the first short here and it turns out this was at spy the spy 413 volatility trigger and here's the second short oops wrong tool the second short set up hero starts to fall and then it took a while but again that 413 level in play so let's go take a look at at book map now so those setups were around 10 am and 10 30 i'm going to zoom in so here's the here the short setups the resistance at the 413 volatility trigger good short setups every time with hero being a a leading indicator traders are taking negative delta positions on in total net market makers were selling futures and batch i still don't understand your question uh all of that what right so batch i'm sorry i don't understand your question i'm just taking a uh you know i guess a pretty simple approach here and looking at what well let me let me back up and talk about how i approach this so i'm looking at at hero here i see this divergence traders taking net negative delta positions in the smb 500 and i'm then i'm looking for a potential reversal level and there it was at the 413 volatility trigger i already know that it acted as acted as resistance once then hero starts dropping there's the second resistance and then hero drops again traders taking negative delta positions as price approaches that resistance level for the third time let's go take a look at book map now zoom out and let's take a look at one other setup somewhere between 11 and 1130 now normally i well what i'm trading i have two screens so i'm looking at i'm looking at hero on one screen and hero on one screen and book map on another screen and this setup at 1130 was not as apparent it was more of a confirmation let's go back and take a look at book map and note i'm also reading order flow here and let's just cover that so here especially at this last setup at um at 1030 note the shift in order flow here green dots market buy orders on the way up those are volume dots showing buy minus sell and green indicates that they're more buyers than sellers and note the shift in order flow as price reaches that 413 level aggressive sellers start to come in you can see the shifts and dots from green to pink and the pink is the color that i use for aggressive sell orders right i looks like truman is trying to answer batches question okay so and you can see the same shift in order flow here just before 1130 reversal at just below vwap let me bump up the liquidity here you can see these limit sell orders here liquidity coming in trying to get filled just below the 4140 resistance level that's spx 4150 and price reverses lower pink dots come in and the price target down at the 4150 level es 4150 so those were the short setups in the smp 500 this morning all right elie asked to use default settings for cvd stops and iceberg tractors below uh i'll tell you what i use for cvd i use the default so that is i've got a number of different cvds i'm not sure why it's showing this one here um for the standard cvd let's see i'm not sure oh here we go there's cvd so this is what i'm using i've i really don't use this i have this shown uh for showing different sizes i did that sometime ago but the the only thing that i've changed is the color so i i like brighter colors here so that's what i'm using for positive and negative and note that the line will shift from positive to negative from blue to uh this pink color and then for the sub chart indicators for stops and icebergs i am using the sum mode and that's really the only change i've changed the colors but i'm using some for both icebergs and stops stops and yellow and sums and blue all right elie i hope that answers your question one other thing that i've started to look at is i normally have the in the past i've been this is in q nastic futures and i have been tracking for everything uh all the instruments in my book map chart here i've been tracking the weekly expected move there's the lower edge the weekly expected move shown with a purple line and there's the upper edge of the expected move and now i have started tracking or adding these blue lines which are the daily expected move here's the lower edge of the daily expected move for in q and these are all based on the options market and this level the for in q has worked very well recently so if you want a an expected range for in q especially uh that's something to keep track of so there's the lower edge of the uh daily expected move and that is for in q and i've got it on the same levels on my es chart here yeah rj that is um yeah that i'll show you where i'm getting that so at the um at the close today at at 5 p.m when when uh future stop trading for an hour then i'll just take that this number so the end of the day i don't know why was that little end of the day i'll look at this number right here and that's for tomorrow that is the right now the one dte look at that number right there and you can look at that in any options chain and that'll that's a plus or minus and then i'll just note that number and i'll update my spreadsheet and uh elie asked do we take this spot gamma reference price posted in the spot gamma am founders note to calculate expected move ranges and yeah you can what what uh he's talking about and let's go to and spot gamma used to provide more uh more information on this and this is so you can use this to calculate uh that expect expected move as well although it's only shown for uh spx and spy i've just been using the it's just a little bit easier to get that information from um from thinkorswim or any i'm sure any other um trading platform with an options chain should show that right let's take a look at some other setups so that is the smb 500 i'm going to look at some stocks here's amd and i'm going to zoom in on the morning session and noted this divergent short setup so heroes falling as price makes a higher high let's go take a look at book map amd and here's the short setup at vwap note the shift in order flow the shift in all the green dots to now pink dots coming in market sell orders reversal at vwap and the 90 putwall key gamma strike price targets at 89 and the price moves lower down at the 88 level and those are high liquidity targets price is attracted to the liquidity what truman says the expected move for the toss option chain is the expected move by expiration and if there are daily options like es and q spx spy and qqq then it is daily so i'm if i'm looking at one dte today that will be for tomorrow and if i'm looking at zero dte that is for today so to set the levels for tomorrow at the end of the day i will look at the one dte note those in my spreadsheet or just write those down and those with the levels for tomorrow that i use that i've been using right so that's amd there's amazon and there are a number of ways that you can do those expected rating trading range at looking at selling premium if trade if price is trading inside those ranges looking at selling an iron condor for example or price reaches one of the daily extreme selling a vertical or um you know any way that you want to approach that so there is amazon let's take a look at hero for amazon and this was another divergent short options traders taking negative delta positions price makes a higher high then reverses lower a couple of short setups there oh just after 10 and around but before 10 30 all right let's take a look at at book map and batch ass there's a big wall at 101 on amazon um by wall if you mean spot gamma level no there is liquidity at 101 and that's shown with the heat map here and in book map those are resting by orders and buyers seek sellers and sellers seek buyers and this liquidity tends to attract price acts as a magnet for price and that's what's so nice about trading stocks is this liquidity comes in often at the rth open and stays there for the remainder of the day until it gets filled if they don't get filled they'll come in the next day all right and rj asked do you have any thoughts on tracking iv versus realize volatility and let me show you what i do so let's go back to thinkorswim let's take a look at spx take a look at a chart and i'm going to take a look at this volatility chart and i have a a number of volatility settings i'm going to zoom in on this and i haven't updated these yet that's the weekly expected move this is what i have been using and i've had this for years this is showing iv compared to historical volatility or realized volatility and as long as the red line is above the blue line that means that fear is overstated that implied volatility is higher than realized volatility so it's a good time for selling selling premium and that's what i use that for so let's zoom back out so anytime let's say right in right in this range here with pretty steady price implied volatility much higher the red line much higher than the blue line a good time for selling volatility and rj asked what's the formula on on realized i have used this script for years i i don't know i'd have to go take a look at it all right and just to point out this a couple of ways of approaching this range day first of all here's an iron condor and that's zero dte options here's a vertical so i'm going to keep an eye on these all right so that is amazon let's take a look at meta go back and take a look at hero and meta was more of a confirmation short right here about 1020 let's go back take a look at book map notice price reached that high traders started taking negative delta positions and there's the reversal at the 220 key gamma strike as traders were taking negative delta positions let's take a look at microsoft and microsoft i thought hero was actually a little bit of a lagging indicator here but after the break of the 290 key gamma strike there was a little bit more clear as hero leveled off let's zoom in on this warning so price moved up hero options traders lagging a little bit as price reached a high hero started to move lower and price dropped pretty quickly below that 290 key gamma strike not as clear a setup as some other stocks and also futures so that's microsoft and e i ask when do you update your price line spreadsheet for the trading day i update it before the rth open so i um on the the levels so first of all i'm getting for stocks let's take a look i'm getting my levels here from equity hub for stocks so the put wall call wall key gamma strike hedge wall uh for stocks those are all updated in the morning and i can update that spreadsheet and uh that's it i'm done for the day for stocks and then for for the smb 500 and qqq your spy for example the spot gamma has these pop-ups and this is showing the key daily levels like put wall volatility trigger call wall and then the key gamma strike is shown in in equity hub here so that is the key daily levels then it's also showing some additional levels and i add those all to my spreadsheet and then i also have in my spreadsheet we go to my stock spreadsheet here spy and then i also have the spx levels shown right in here and i will that ratio the spx spy ratio does not change that much from day to day so i start with the the number wrong tool i start with the number that i had yesterday if any of these levels change and it's pretty close so that is my that's my spry set up the same for qqq and then for futures i have just the same same spx levels then i'm also showing the key spy levels and all of this i can update before the open and then i just check the ratios and the spx es difference and if i have to make any changes it will be minor from day to day so i can do this all before the market opens and then make minor minor changes based on any changes in the es spx difference or price ratios after after the open all right let's take a look at qqq first thing in the morning there was a nice divergent short just in the first 30 minutes notice hero dropping immediately from the open traders taking negative delta positions at the open and that set up a nice short just uh no a few minutes after the open let's go take a look at a qqq and book map and there's the short set up at this 319c one level and that is a combo one level one being the most important in a scale of one to five so a quick run up to that level and then a short another opportunity to short there let's take a look at tesla let's take a look at spy and i have the same levels on spy my spy chart as i do on the es chart so there's the spy 4 413 volatility trigger resistance level there's the spx 4150 notice resistance level in the spot gamma am founders note so definitely not a lot of range today it's sort of a range day with a bearish bias so those are the how the levels that i uh so the levels on my spy chart so i can trade spy or es just looking at the chart here and then let's wrap it up let's take a look at tesla and as usual the stocks that i trade tesla and video uh are the most volatile have the most range let's take a look at hero tesla and as usual with tesla there's a very strong correlation between options trades hedging flow and price action and this is separating puts and calls the orange line is showing call transactions and the blue line is showing put transactions and what this is showing is pretty much from the open a couple of 10 minutes after the open trader started buying puts initially they were buying calls rising orange line they started selling calls and price moved lower setting up the short right here note the buy sweep all these small green dots that buy sweep up to the one night 89 level and then price reverses lower let me just zoom in on this section right here and note the shift in order flow big pink dot comes in more pink dots and order flow finally shifts bearish that's right rj traders were definitely buying puts looking for lower prices in tesla let's take one final look at hero look at the total numbers here this notional value 47.5 million positive 47 point now 7 million versus minus 68.1 million for puts so net net put buyers are winning all right so elie ask orange line up traders buying calls dealer short calls yes that is uh that is what that means so the lines are shown in terms of delta so rising orange line means that traders are buying calls market makers have to they sell the calls taking the other side of the trade and they have to buy stock to hedge their delta exposure all right so truman ask can you stay in tesla by what hero shows as long there's not a divergence i um i really don't see much of a divergence uh typically with with tesla tesla you're looking at more of a confirmation the hero line shown in purple tracks the price line pretty closely and tomie ask are those charts in real time yes so that is this is hero h i r o hedging impact real time options and elie ask blue line down traders are buying puts dealers are selling puts and yes that is correct so think of these lines always in terms of delta so a positive trade would be traders are buying calls and or selling puts that's positive delta and negative delta is selling calls and buying puts and again market makers are taking the other side of those trades let's just go back and take a look at the s and p 500 one more time in rj that let me take a look at your question after after the webinar i need to wrap it up so i'll i'll take a look at your question and and see if i can answer that um and truman says your class always go by goes by fast uh i think that's a good thing well i i guess i i guess so if it if it's interesting all right i'm going to wrap it up uh that's my time is up and i want to thank you for watching thanks for your questions and comments and i will see you tomorrow thanks again bye