Reducing Variance in Hobson and Rogers Model for Option Pricing

This paper investigates the use of a variance reduction, called importance sampling, for Monte Carlo methods in the case of the stochas- tic volatility model for option pricing introduced by Hobson and Rogers (1998). We brie°y recall that a European call option contract gives the right, but not the obligation, to buy a speci¯c amount of a given stock or index at a speci¯ed price (strike price) in a speci¯ed 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 stochas- tic 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 num- ber generators. It is shown, ¯nally, that variance is dramatically reduced meaning that numerical techniques introduced for variance reduction have still a lot to say.