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A General Framework for Pricing Asian Options Under Markov Processes

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
  • Handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:540-554
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    File URL: http://dx.doi.org/10.1287/opre.2015.1385
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    1. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    2. repec:eee:ejores:v:266:y:2018:i:3:p:1134-1139 is not listed on IDEAS
    3. repec:eee:phsmap:v:507:y:2018:i:c:p:175-191 is not listed on IDEAS
    4. Nabil Kahale, 2018. "General multilevel Monte Carlo methods for pricing discretely monitored Asian options," Papers 1805.09427, arXiv.org, revised Sep 2018.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models (Revised version of CARF-F-365 : Subsequently published in Mathematics of Operations Research)," CARF F-Series CARF-F-426, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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