Counterparty Risk - PFE Calculation

Magnumpi · September 4th, 2012, 7:37 am

Hi All,I'am new on counterparty risk and I'm trying to understand how to deal with PFE calculation. Let's say that we have a plain vanilla call option on a stock with maturity 2 yr and we want to value the exposure at certain points between 0 and 2 yr.I know that I have to simulate, through Monte Carlo Simulations, the underlying stock price but after that how can I determine the distribution of the exposure at each intermediate point in time?Thank you!!!

gileper · September 5th, 2012, 7:08 am

plain vanilla call option price is monotonic with respect the stock price, hence there is a one to one mapping between the quantiles of the stock price distribution and the (unknown) call price distribution. Find the quantile of the stock and plug it in BS formula.best

Magnumpi · September 6th, 2012, 6:20 am

thank you for your answer!!!!Then if I want to calculate the Expected Exposore(EE(t)) at each time step I have basically to perform a number N of Black and Scholes pricing equal to the number of underlying simulations.Is it correct?Bye

gileper · September 6th, 2012, 10:10 am

You are welcome.1) As regarding the pfe you dont need to simulate you get a closed formula.2) Yes, if you want to compute the EE you need to simulate the stock price at t, plug it in BS, loop n-times and then average the vector of the call prices.Of course you can NOT compute the E(St) and then plug in BS because of Jensen E[C(st)] != C[E[St]]