A General Framework for Pricing Asian Options Under Markov Processes

Ning Cai (), Yingda Song () and Steven Kou ()
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Ning Cai: Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
Yingda Song: Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China
Steven Kou: Risk Management Institute and Department of Mathematics, National University of Singapore, Singapore 119077

Operations Research, 2015, vol. 63, issue 3, 540-554

Abstract: 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.

Keywords: finance; asset pricing; probability; stochastic model applications (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (55)

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