IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1811.11379.html
   My bibliography  Save this paper

Option Pricing in a Regime Switching Jump Diffusion Model

Author

Listed:
  • Anindya Goswami
  • Omkar Manjarekar
  • Anjana R

Abstract

This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, driving the values of interest rate and volatility coefficient. The pure jump process is assumed to be a semi-Markov process on finite state space. This consideration helps to incorporate a specific type of memory influence in the asset price. Under this model assumption, the locally risk minimizing price of the European type path-independent options is found. The F\"{o}llmer-Schweizer decomposition is adopted to show that the option price satisfies an evolution problem, as a function of time, stock price, market regime, and the stagnancy period. To be more precise, the evolution problem involves a linear, parabolic, degenerate and non-local system of integro-partial differential equations. We have established existence and uniqueness of classical solution to the evolution problem in an appropriate class.

Suggested Citation

  • Anindya Goswami & Omkar Manjarekar & Anjana R, 2018. "Option Pricing in a Regime Switching Jump Diffusion Model," Papers 1811.11379, arXiv.org, revised Oct 2019.
  • Handle: RePEc:arx:papers:1811.11379
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1811.11379
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anindya Goswami & Sanket Nandan, 2015. "Convergence of Estimated Option Price in a Regime switching Market," Papers 1506.03621, arXiv.org, revised Mar 2016.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    3. Arunangshu Biswas & Anindya Goswami & Ludger Overbeck, 2017. "Option Pricing in a Regime Switching Stochastic Volatility Model," Papers 1707.01237, arXiv.org, revised Jan 2018.
    4. Anindya Goswami & Jeeten Patel & Poorva Shevgaonkar, 2015. "A system of non-local parabolic PDE and application to option pricing," Papers 1506.01467, arXiv.org, revised May 2016.
    5. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    6. Chang-Jin Kim & Charles R. Nelson, 1998. "Business Cycle Turning Points, A New Coincident Index, And Tests Of Duration Dependence Based On A Dynamic Factor Model With Regime Switching," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 188-201, May.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    9. Hunt, Julien & Devolder, Pierre, 2011. "Semi-Markov regime switching interest rate models and minimal entropy measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3767-3781.
    10. Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
    11. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    12. Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
    13. Biswas, Arunangshu & Goswami, Anindya & Overbeck, Ludger, 2018. "Option pricing in a regime switching stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 116-126.
    14. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
    15. Bardhan, Indrajit & Chao, Xiulu, 1993. "Pricing options on securities with discontinuous returns," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 123-137, October.
    16. Milan Kumar Das & Anindya Goswami & Tanmay S. Patankar, 2016. "Pricing Derivatives in a Regime Switching Market with Time Inhomogeneous Volatility," Papers 1611.02026, arXiv.org.
    17. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    18. Tanmay S. Patankar, 2016. "Asset Pricing in a Semi-Markov Modulated Market with Time-dependent Volatility," Papers 1609.04907, arXiv.org.
    19. Hunt, Julien & Devolder, Pierre, 2011. "Semi Markov regime switching interest rate models and minimal entropy measure," LIDAM Discussion Papers ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Aase, Knut K., 1988. "Contingent claims valuation when the security price is a combination of an Ito process and a random point process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 185-220, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Samuel Drapeau & Yunbo Zhang, 2019. "Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model," Papers 1910.08344, arXiv.org, revised May 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Milan Kumar Das & Anindya Goswami, 2019. "Testing of binary regime switching models using squeeze duration analysis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-20, March.
    2. Milan Kumar Das & Anindya Goswami, 2018. "Testing of Binary Regime Switching Models using Squeeze Duration Analysis," Papers 1807.04393, arXiv.org, revised Aug 2018.
    3. Milan Kumar Das & Anindya Goswami & Sharan Rajani, 2019. "Inference of Binary Regime Models with Jump Discontinuities," Papers 1910.10606, arXiv.org, revised Mar 2022.
    4. Biswas, Arunangshu & Goswami, Anindya & Overbeck, Ludger, 2018. "Option pricing in a regime switching stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 116-126.
    5. Anindya Goswami & Kedar Nath Mukherjee & Irvine Homi Patalwala & Sanjay N. S, 2022. "Regime recovery using implied volatility in Markov modulated market model," Papers 2201.10304, arXiv.org, revised Mar 2022.
    6. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    7. Arunangshu Biswas & Anindya Goswami & Ludger Overbeck, 2017. "Option Pricing in a Regime Switching Stochastic Volatility Model," Papers 1707.01237, arXiv.org, revised Jan 2018.
    8. Milan Kumar Das & Anindya Goswami & Sharan Rajani, 2023. "Inference of Binary Regime Models with Jump Discontinuities," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 49-86, May.
    9. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.
    10. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing lookback options with regime switching," Papers 1407.4864, arXiv.org.
    11. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    12. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    13. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    14. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
    15. Wei Wang & Linyi Qian & Wensheng Wang, 2016. "Hedging of contingent claims written on non traded assets under Markov-modulated models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3577-3595, June.
    16. Su-Lien Lu & Kuo-Jung Lee, 2021. "Investigating the Determinants of Credit Spread Using a Markov Regime-Switching Model: Evidence from Banks in Taiwan," Sustainability, MDPI, vol. 13(17), pages 1-25, August.
    17. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    18. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2013. "On pricing basket credit default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1845-1854, December.
    19. Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
    20. Anatoliy Swishchuk & Maksym Tertychnyi & Robert Elliott, 2014. "Pricing Currency Derivatives with Markov-modulated Levy Dynamics," Papers 1402.1953, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1811.11379. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.