However, as we know from Slide 10, this masks substantial changes in the underlying density forecasts, with the lower rate mode becoming more prominent. 50  See e.g. Crump et al. (2014), and more recently Brodsky et al. (2016a). 51  Market-implied rates were derived from futures prices at the same time as responses were received from the surveys. 52  Adrian, Crump, and Moench (2013). 14  BIS central bankers’ speeches  Finance models make a variety of assumptions that allows them to extract risk premia from asset prices. Once that is done, they can obtain the underlying so-called “physical” probability distribution of the marginal investor – that is, the actual probability she assigns to various outcomes. Brodsky et al. propose a complementary approach, called “tilting,” which is, in a way, the reverse of the finance approach.53 It starts from the survey probability distribution and asks: How much do I have to “tilt” the original distribution – that is, how much probability mass do I have to shift around – to obtain the market-implied path as its mean? There are many ways to tilt or alter the survey distribution such that its mean is the market rate. Our approach is to require that the tilted distribution is as close as possible to the original survey distribution, where the notion of distance is one that is commonly used in statistics, and is based on a measure called relative entropy or Kullback-Leibler information criterion (KLIC). This relative entropy approach is nothing new.
Next Steps  I started this talk by noting that we may be in the midst of a leap forwards in payments. This is good news. Innovation – including the innovation some of you in this room are pushing forward as part of the New Payments Architecture project, and the work that the Bank of England is pursuing on RTGS renewal promises to deliver easier, faster, cheaper, and more stable payments. But to ensure that this period of innovation does not end in a leap backwards we need to be sure that regulation keeps pace. Regulation needs to facilitate innovation by avoiding picking winners or losers. Instead we should focus on delivering same risk, same regulation. The protections regulation delivers for your payments should not depend on whether you are paying by cash, card, interbank, or stablecoin. Fortunately, here in the UK we have an opportunity to ensure that regulation remains fit for purpose through this period of change. HM Treasury is currently leading a welcome review of the payments landscape. And there is related work underway in the cross-authority Cryptoassets Task Force that was launched by 7  All speeches are available online at www.bankofengland.co.uk/news/speeches  7  HM Treasury in 2018, bringing together Bank, FCA and Treasury thinking. The Bank of England’s Financial Policy Committee is supporting this work by providing insight into the financial stability implications of innovation in payments – in December, for the first time ever, its semi-annual Financial Stability Report included a chapter on payments.