An Analytical Method for Multi-Asset Option Pricing Based on a Single-Factor Model

作者：Ye Letian^*

来源：Journal of Derivatives, 2016, 24(1): 7-16.

DOI：10.3905/jod.2016.24.1.007

This article introduces an analytical method for multi-asset European options under a single factor model assumption that posits that the return on assets can be decomposed into the sum of a constant value, the return on a single common factor and an independent residual return (the error term). Based on the single factor model's conditional independence, the exact analytical results are generated for a rainbow option, the nth best-of-N-assets option, and the approximate analytical results for a basket option, which are close to Monte Carlo simulation results. A Gaussian copula is employed to relax the lognormal distribution assumption. Finally, this article discusses how to estimate the correlation factor and proposes an algorithm to calibrate the correlation factor from the correlation matrix. The method introduced in this article is useful because of its accurate results, its weak condition, its easy implementation, and its efficiency when N is large; moreover, it is precise and its error can be evaluated even when the single factor model cannot be satisfied. This algorithm can be extended to a multi factor model that is more accurate but also complex.

• 出版日期2016
• 单位清华大学