April 30th, 2012, 11:42 am
Hello!I have calculated the implied risk-neutral density of by using Dupire's formula (or whatever you want to call it ):I have market data at time T consisting of 9 different call prices corresponding to 9 different strike prices, volatilities and the rate at time T. I estimated the second derivative using these data points. Now I would like to compare it to the distribution of in the Black-Scholes model. Since is log-normal that is:it is easy to derive an explicit expression for the density function of Now here comes my question. I'm unsure about how to pick the parameters in this equation. Since I shall compare it with the implied density it must be reasonable to have r as the market rate at time T, S0 as the stock price at the first day of the option contracts. But how should I pick sigma? I have 9 different market volatilities. Is it a good idea to just take the mean of these?I appreciate any input!Thank you in advance!
Last edited by
DoubleTrouble on April 29th, 2012, 10:00 pm, edited 1 time in total.