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

Author

Listed:
  • Kenichiro Shiraya

    (The University of Tokyo)

  • Akihiko Takahashi

    (The University of Tokyo)

Abstract

This paper presents a new approximation formula for pricing discretely monitored average options and spread options in a local-stochastic volatility (LSV) model with jumps. Particularly, our model includes local-volatility functions and jump components in both the underlying asset price and its volatility processes. To the best of our knowledge, the proposed approximation is the first one which achieves analytic approximations for the average and spread option prices in this environment. In numerical experiments, by employing several models we provide approximate prices for average and calendar spread options on the WTI futures based on the parameters through calibration to the listed (plain-vanilla) futures option prices, and compare those with the CME settlement prices, which confirms the validity of the method. Moreover, we show the LSV with jumps 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, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CARF F-Series CARF-F-365, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf365
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    References listed on IDEAS

    as
    1. Ning Cai & Chenxu Li & Chao Shi, 2014. "Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 789-822, August.
    2. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Pricing Multiasset Cross‐Currency Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(1), pages 1-19, January.
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    7. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    8. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    9. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    10. Kenichiro Shiraya & Akihiko Takahashi, 2011. "Pricing average options on commodities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(5), pages 407-439, May.
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