Option Pricing Under GARCH Processes Using PDE Methods

• 成果类型: Article
• 署名作者: Breton, Michele; de Frutos, Javier
• 署名单位: Universite de Montreal; Universite de Montreal; HEC Montreal; Universidad de Valladolid
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1100.0822
• 发表日期: 2010
• 页码: 1148-1157
• 关键词: simulation

摘要

In this paper, we propose a partial differential equation formulation for the value of an option when the underlying asset price is described by a discrete-time GARCH process. Our numerical approach involves a spectral Fourier-Chebyshev interpolation. Numerical illustrations are provided, and the results are compared with other available valuation methods. Our numerical procedure converges exponentially fast and allows for the efficient computation of option prices, achieving a high level of precision in a few seconds of computing time.