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Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions

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  • Dongdong Hu
  • Hasanjan Sayit
  • Svetlozar T. Rachev

Abstract

The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas for the price of spread options under exponential L\'evy models with mean-variance mixture. Unlike the semi-closed form formulas in Caldana and Fusai [5], where spread prices were expressed by using Fourier inversion formula for general price dynamics, our formula expresses spread prices in terms of the mixing distribution. Numerical tests show that our formulas give accurate spread prices also

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  • Dongdong Hu & Hasanjan Sayit & Svetlozar T. Rachev, 2021. "Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions," Papers 2109.02872, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2109.02872
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    References listed on IDEAS

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    1. Charles J. Corrado & Tie Su, 1996. "S&P 500 index option tests of Jarrow and Rudd's approximate option valuation formula," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(6), pages 611-629, September.
    2. Emmanuel Jurczenko & Bertrand Maillet & Bogdan Negrea, 2004. "A note on skewness and kurtosis adjusted option pricing models under the Martingale restriction," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 479-488.
    3. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    4. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    5. Bjerksund, Petter & Stensland, Gunnar, 2006. "Closed form spread option valuation," Discussion Papers 2006/20, Norwegian School of Economics, Department of Business and Management Science.
    6. Laurence Carassus & Miklós Rásonyi, 2020. "Risk-Neutral Pricing for Arbitrage Pricing Theory," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 248-263, July.
    7. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    8. Petter Bjerksund & Gunnar Stensland, 2014. "Closed form spread option valuation," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1785-1794, October.
    9. Bertrand Maillet & Bogdan Négréa, 2004. "A Note on Skewness and Kurtosis Adjusted Option Pricing Models under the Martingale Restriction," Post-Print hal-00308980, HAL.
    10. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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