Asymptotics beats Monte Carlo: the case of correlated local vol baskets (Q2922151)

The authors consider the problem of pricing a European option on a basket of assets. It is assumed that the prices of the assets are described by CEV (constant elasticity of variance) processes, possibly correlated. Unlike in other works, the assets in the basket can have positive and negative weights. They propose a numerical procedure based on solving partial differential equations describing the transition density function. To this end the authors use asymptotic methods based on a heat kernel expansion. With this approach, they derive the methods for calculating price and implied volatility of the option.NEWLINENEWLINEThe authors compare their method with a pricing by Monte Carlo simulation. The results of the numerical analysis show that their method is fairly accurate and much faster: it gives a result in a few seconds in cases when Monte Carlo simulations requires a week. Although the accuracy decreases with the time to maturity of an option, the authors show (on random examples) that the relative error is on the third decimal place for a maturity of 2 years and on the second decimal place for a maturity of 10 years.