Variance Reduction in a Stochastic Volatility Scenario

This paper investigates the use of a variance reduction, called importance sampling, for Monte Carlo methods in the case of the stochastic volatility model for option pricing introduced by Hobson and Rogers (1998). We briefly recall that a European call option contract gives the right, but not the obligation, to buy a specific amount of a given stock or index at a specified price (strike price) in a specified time (maturity); we show some evidence on the call options on MIB30 Italian Index to verify the performance of the importance sampling in a complete stochastic volatility model. In Monte Carlo method the price of a call option is obtained as the average value of the simulations of a large number of independent, uniform variates (prices) by means of pseudo-random number generators. It is shown, finally, that variance is dramatically reduced meaning that numerical techniques introduced for variance reduction have still a lot to say.