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Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models

Author

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  • Kenichiro Shiraya

    (Graduate School of Economics, University of Tokyo, Bunkyou-ku, Tokyo, 113-0033, Japan)

  • Akihiko Takahashi

    (Graduate School of Economics, University of Tokyo, Bunkyou-ku, Tokyo, 113-0033, Japan)

Abstract

This paper presents a new approximation formula for pricing multidimensional discretely monitored average options in a local-stochastic volatility (LSV) model with jump by applying an asymptotic expansion technique. Moreover, it provides a justification of the approximation method with some asymptotic error estimates for general payoff functions. Particularly, our model includes local volatility functions and jump components in the underlying asset price as well as its volatility processes. To the best of our knowledge, the proposed approximation is the first one that achieves analytic approximations for the average option prices in this environment. In numerical experiments, by employing several models, we provide approximate prices for the listed average and calendar spread options on the West Texas Intermediate (WTI) futures based on the parameters through calibration to the listed (plain-vanilla) futures options prices. Then, we compare those with the Chicago Mercantile Exchange (CME) settlement prices, which confirms the validity of the method. Moreover, we show that the LSV with jump model is able to replicate consistently and precisely listed futures option, calendar spread option, and average option prices with common parameters.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2019. "Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 303-333, February.
    • Handle: RePEc:inm:ormoor:v:44:y:2019:i:1:p:303-333
    DOI: 10.1287/moor.2017.0925
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    References listed on IDEAS

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    14. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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    2. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.
    3. Alev{s} v{C}ern'y & Johannes Ruf, 2019. "Simplified stochastic calculus with applications in Economics and Finance," Papers 1912.03651, arXiv.org, revised Jan 2021.

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