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Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets

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  • Semere Habtemicael

    (Department of Applied Mathematics, Wentworth Institute of Technology, Boston, MA 02115, United States)

  • Indranil SenGupta

    (Department of Mathematics, North Dakota State University, Fargo, ND 58108-6050, United States)

Abstract

The objective of this paper is to study the arbitrage free pricing of variance and volatility swaps for Barndorff-Nielsen and Shephard type Lévy process driven financial markets. One of the major challenges in arbitrage free pricing of swap is to obtain an accurate pricing expression which can be used with good computational accuracy. In this paper, we obtain various approximate expressions for the pricing of volatility and variance swaps. We show that with the approximate formulas obtained from the Barndorff-Nielsen and Shephard model the error estimation in fitting the delivery price is much less than the existing models with comparable parameters. Pricing formulas proposed in this paper are simple to compute in real time and hence can be efficiently used in practical applications. Numerical results are provided in support of the accuracy of approximate formulas presented in this paper.

Suggested Citation

  • Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:04:n:s2424786316500274
    DOI: 10.1142/S2424786316500274
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    Citations

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    Cited by:

    1. Chen Mao & Guanqi Liu & Yuwen Wang, 2021. "A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    2. Michael Roberts & Indranil SenGupta, 2020. "Sequential hypothesis testing in machine learning, and crude oil price jump size detection," Papers 2004.08889, arXiv.org, revised Dec 2020.
    3. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    4. Michael Roberts & Indranil SenGupta, 2020. "Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing," Annals of Finance, Springer, vol. 16(1), pages 121-139, March.
    5. Takuji Arai, 2019. "Pricing And Hedging Of Vix Options For Barndorff-Nielsen And Shephard Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-26, December.
    6. Semere Habtemicael & Musie Ghebremichael & Indranil SenGupta, 2019. "Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 75-92, June.
    7. Michael Roberts & Indranil SenGupta, 2019. "Infinitesimal generators for two-dimensional L\'evy process-driven hypothesis testing," Papers 1911.08412, arXiv.org.
    8. Takuji Arai, 2019. "Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models," Papers 1904.12260, arXiv.org.
    9. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    10. Humayra Shoshi & Indranil SenGupta, 2020. "Hedging and machine learning driven crude oil data analysis using a refined Barndorff-Nielsen and Shephard model," Papers 2004.14862, arXiv.org, revised Feb 2021.
    11. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Papers 2105.02325, arXiv.org.
    12. Shubham Ekapure & Nuruddin Jiruwala & Sohan Patnaik & Indranil SenGupta, 2021. "A data-science-driven short-term analysis of Amazon, Apple, Google, and Microsoft stocks," Papers 2107.14695, arXiv.org.
    13. Treena Basu & Olaf Menzer & Joshua Ward & Indranil SenGupta, 2022. "A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series," Risks, MDPI, vol. 10(2), pages 1-16, February.
    14. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Annals of Finance, Springer, vol. 17(4), pages 529-558, December.
    15. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    16. Anatoliy Swishchuk & Zijia Wang, 2017. "Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models," Papers 1712.02735, arXiv.org.

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