text: A version of this formula is used in the first step of deriving the Black-Scholes model to establish the equation for delta V. Faa di Bruno's formula is a higher-level generalization of this formula, whose counterpart in stochastic calculus is called Ito’s Lemma.
full_question: A version of this formula is used in the first step of deriving the Black-Scholes model to establish the equation for delta V. Faa di Bruno's formula is a higher-level generalization of this formula, whose counterpart in stochastic calculus is called Ito’s Lemma. By this formula, the Jacobian of the composition of two functions is equal to the product of each function’s Jacobian. Using this rule and the product rule, one can derive the quotient rule. For 10 points, name this calculus “rule” which states that the derivative of f of g of x is f prime of g of x multiplied by g prime of x.
first_sentence: A version of this formula is used in the first step of deriving the Black-Scholes model to establish the equation for delta V. Faa di Bruno's formula is a higher-level generalization of this formula, whose counterpart in stochastic calculus is called Ito’s Lemma.