Sunday, September 1, 2019

stochastic calculus - How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?


I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs


$$(S_T f(S_T))^+$$


How do I express the stock dynamics using the stock as numéraire, and how do I get the stock distribution under the equivalent measure.




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