Weak approximation of stochastic differential equations and application to derivative pricing

TL;DR

This paper introduces a simple algorithm for approximating weak solutions of stochastic differential equations, demonstrating its effectiveness in fast Asian option pricing under the Heston model using quasi-Monte Carlo methods.

Contribution

It proposes a novel, straightforward algorithm for weak approximation of SDEs and shows its application to efficient derivative pricing with enhanced computational speed.

Findings

Algorithm achieves faster computations for derivative pricing.

Combining the algorithm with quasi-Monte Carlo methods improves efficiency.

Application to Asian options under the Heston model demonstrates practical effectiveness.

Abstract

The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast. [1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198.