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Generalized Bn–S Stochastic Volatility Model For Option Pricing

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  • INDRANIL SENGUPTA

    (Department of Mathematics, North Dakota State University, NDSU Dept # 2750, Minard Hall 408E12, Fargo, ND 58108-6050, USA)

Abstract

In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:02:n:s021902491650014x
    DOI: 10.1142/S021902491650014X
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    References listed on IDEAS

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    11. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
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    Cited by:

    1. 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.
    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. Subhojit Biswas & Diganta Mukherjee & Indranil SenGupta, 2020. "Multi-asset Generalised Variance Swaps in Barndorff-Nielsen and Shephard model," Papers 2011.13474, arXiv.org.
    4. 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.
    5. 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.
    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. 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.
    8. Oliver Pfante & Nils Bertschinger, 2019. "Volatility Inference And Return Dependencies In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-44, May.
    9. 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.
    10. 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.
    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.

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