Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

Abstract

A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model.

2000 Mathematics Subject Classification, 65C30, 65C05.

Keywords:

• Heston model
• numerical methods for stochastic differential equations
• mathematical finance
• quasi‐Monte Carlo method

Acknowledgement

This research was partially supported by the Japanese Ministry of Education, Science, Sports and Culture, Grant‐in‐Aid for Scientific Research (C), 15540110, 2003.