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

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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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    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. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    3. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    4. 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.
    5. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    6. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    7. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    8. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    9. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    10. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    11. Akihiko Takahashi & Toshihiro Yamada, 2015. "On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 513-541, March.
    12. 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.
    13. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.
    14. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    15. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    16. Cass, Thomas, 2009. "Smooth densities for solutions to stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1416-1435, May.
    17. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    18. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models Online Appendix," CARF F-Series CARF-F-412, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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    2. 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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