We will apply the Monte Carlo simulation method. Data: we will price a call option on the S&P 500 index. The index level at the close of yesterday was equal to 1,065. Assume an annualized long term volatility for the index of 20% per year. The 1-year LIBOR rate is at 1.25%. For the stochastic volatility process take a = 0.95 and c = 0.85. Objective: we want to price several European call options on the S&P 500 index with maturity equal to 1 year (250 trading days) and strike prices between 100 and 2000. We will do this under different correlation scenarios. The purpose is to show how a stochastic volatility process can generate model prices that exhibit a Black-Scholes implied volatility smile.

6. Now we are going to repeat the exercise but compute SVM prices under two alternative scenarios. For the first alternative, change the correlation from -30% to 0. Compute implied volatilities and implied distribution and compare them to the SVM scenario where = 30%. What changes?