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Computable Error Bounds of Laplace Inversion for Pricing Asian Options

Author

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  • Yingda Song

    (Antai College of Economics and Management, Shanghai Jiao Tong University, 200030 Shanghai, China)

  • Ning Cai

    (Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China)

  • Steven Kou

    (Risk Management Institute and Department of Mathematics, National University of Singapore, Singapore; National University of Singapore Suzhou Research Institute, Suzhou Industrial Park, 215123 Suzhou, China)

Abstract

The prices of Asian options, which are among the most important options in financial engineering, can often be written in terms of Laplace transforms. However, computable error bounds of the Laplace inversions are rarely available to guarantee their accuracy. We conduct a thorough analysis of the inversion of the Laplace transforms for continuously and discretely monitored Asian option prices under general continuous-time Markov chains (CTMCs), which can be used to approximate any one-dimensional Markov process. More precisely, we derive computable bounds for the discretization and truncation errors involved in the inversion of Laplace transforms. Numerical results indicate that the algorithm is fast and easy to implement, and the computable error bounds are especially suitable to provide benchmark prices under CTMCs. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0805 .

Suggested Citation

  • Yingda Song & Ning Cai & Steven Kou, 2018. "Computable Error Bounds of Laplace Inversion for Pricing Asian Options," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 634-645, January.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:4:p:634-645
    DOI: 10.1287/ijoc.2017.0805
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    References listed on IDEAS

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    3. Zhang, Xiang & Li, Lingfei & Zhang, Gongqiu, 2021. "Pricing American drawdown options under Markov models," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1188-1205.
    4. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    5. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    6. Gongqiu Zhang & Lingfei Li, 2023. "A general approach for Parisian stopping times under Markov processes," Finance and Stochastics, Springer, vol. 27(3), pages 769-829, July.
    7. Wensheng Yang & Jingtang Ma & Zhenyu Cui, 2021. "Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 359-412, April.
    8. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.

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