Asymptotic expansion method for pricing and hedging American options with two-factor stochastic volatilities and stochastic interest rate

摘要

We consider the pricing and hedging of American put options under the double Heston model with CIR stochastic interest rate. With an explicit exercise rule American option is approximated by barrier option for which the solution to the partial differential equation is derived by a short-maturity asymptotic expansion. Combining with control variate technique by Fourier-cosine expansion we analytically derive American puts prices and hedging parameters. We also construct a Delta-Vega-Rho hedging strategy of the proposed model for American puts and implement it by Monte Carlo simulation. Numerical results show that the presented pricing method is fast and accurate, the hedging performance of the proposed model is better than that of the BS, Heston and double Heston model.