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Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes

Author

Listed:
  • Semere Habtemicael

    (Wentworth Institute of Technology)

  • Musie Ghebremichael

    (Harvard Medical School
    Ragon Institute of MGH, MIT, Harvard)

  • Indranil SenGupta

    (North Dakota State University)

Abstract

The main goal of this paper is to model variance and volatility swap using superposition of Barndorff-Nielsen and Shephard (BN-S) type models. In particular, in this paper we propose superposition of Lévy process driven by Γ(ν,α) and Inverse Gaussian distributions. Model performance is assessed on data not used to build the model (i.e., test data). It is shown that the prediction error rate for the models considered in this paper are much lower compared to those from previous related models. Moreover, it is shown that unlike previous related models which are restricted to stable markets, the present approach can be applied to both stable and unstable markets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-017-0145-y
    DOI: 10.1007/s13571-017-0145-y
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    References listed on IDEAS

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    1. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466, October.
    2. 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.
    3. 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.
    4. Mariani, Maria C. & Tweneboah, Osei K., 2016. "Stochastic differential equations applied to the study of geophysical and financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 170-178.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    6. Semere Habtemicael & Indranil Sengupta, 2016. "Pricing Covariance Swaps For Barndorff–Nielsen And Shephard Process Driven Financial Markets," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-32, September.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    8. Indranil Sengupta, 2016. "Generalized Bn–S Stochastic Volatility Model For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-23, March.
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    Citations

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    Cited by:

    1. Xianfei Hui & Baiqing Sun & Indranil SenGupta & Yan Zhou & Hui Jiang, 2022. "Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning," Papers 2204.02891, arXiv.org, revised Jan 2023.
    2. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    3. Indranil SenGupta & William Nganje & Erik Hanson, 2021. "Refinements of Barndorff-Nielsen and Shephard Model: An Analysis of Crude Oil Price with Machine Learning," Annals of Data Science, Springer, vol. 8(1), pages 39-55, March.
    4. 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.

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