No abstract

Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

This paper studies the control variate method for pricing interest rate derivatives driven by the LIBOR market model. Several control variates are constructed based on distinctive approximations for the LIBOR market model. Numerical results show the great efficiency of our methods. The idea in this paper can also be extended to price other interest rate derivatives under the LIBOR market model, such as Swaptions, Caps, some path dependent interest rate derivatives, and so forth.