A General Framework for Pricing Asian Options Under Markov Processes

• 成果类型: Article
• 署名作者: Cai, Ning; Song, Yingda; Kou, Steven
• 署名单位: Hong Kong University of Science & Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore; National University of Singapore
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2015.1385
• 发表日期: 2015
• 页码: 540-554
• 关键词: expansions; returns

摘要

A general framework is proposed for pricing both continuously and discretely monitored Asian options under one-dimensional Markov processes. For each type (continuously monitored or discretely monitored), we derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. In the special case of continuous-time Markov chain (CTMC), the functional equation reduces to a linear system that can be solved analytically via matrix inversion. Thus the Asian option prices under a one-dimensional Markov process can be obtained by first constructing a CTMC to approximate the targeted Markov process model, and then computing the Asian option prices under the approximate CTMC by numerically inverting the double transforms. Numerical experiments indicate that our pricing method is accurate and fast under popular Markov process models, including the CIR model, the CEV model, Merton's jump diffusion model, the double-exponential jump diffusion model, the variance gamma model, and the CGMY model.