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Vulnerable options with regime switching and stochastic liquidity

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  • He, Xin-Jiang
  • Pasricha, Puneet
  • Lu, Tuantuan
  • Lin, Sha

Abstract

Investigating default risk in pricing options holds significant practical importance, as nearly all market participants and institutions face credit risk. Additionally, economic cycles and asset liquidity are crucial factors that should be incorporated. This paper considers these factors and derives an analytical pricing formula. Specifically, we model the economic cycles through switching volatility driven by a continuous-time Markov chain, while we adopt a discounting factor based on market liquidity levels to model the asset liquidity. We establish a risk-neutral measure after embracing a regime-switching Esscher transform, and formulate a price representation to value vulnerable options analytically despite the complexity of the developed model. We conduct several numerical experiments to validate the model’s efficacy and flexibility.

Suggested Citation

  • He, Xin-Jiang & Pasricha, Puneet & Lu, Tuantuan & Lin, Sha, 2024. "Vulnerable options with regime switching and stochastic liquidity," The Quarterly Review of Economics and Finance, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:quaeco:v:98:y:2024:i:c:s1062976924001364
    DOI: 10.1016/j.qref.2024.101930
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    as
    1. Acharya, Viral V. & Pedersen, Lasse Heje, 2005. "Asset pricing with liquidity risk," Journal of Financial Economics, Elsevier, vol. 77(2), pages 375-410, August.
    2. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    3. Kai Li & Chenjie Xu, 2022. "Regime shifts in a long-run risks model of stock and treasury bond markets," China Finance Review International, Emerald Group Publishing Limited, vol. 12(4), pages 541-570, August.
    4. Sha Lin & Xin‐Jiang He, 2024. "Closed‐Form Formulae for Variance and Volatility Swaps Under Stochastic Volatility With Stochastic Liquidity Risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1447-1461, August.
    5. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    6. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    7. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    8. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    9. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    10. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    11. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    12. Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    13. Raheel Safdar & Sultan Sikandar Mirza & Tanveer Ahsan, 2019. "Market pricing of liquidity risk: evidence from China," Post-Print hal-02463088, HAL.
    14. Lee, Min-Ku & Yang, Sung-Jin & Kim, Jeong-Hoon, 2016. "A closed form solution for vulnerable options with Heston’s stochastic volatility," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 23-27.
    15. Yang Zhao & Jin-Ping Lee & Min-Teh Yu, 2021. "Catastrophe risk, reinsurance and securitized risk-transfer solutions: a review," China Finance Review International, Emerald Group Publishing Limited, vol. 11(4), pages 449-473, August.
    16. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    17. 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.
    18. Puneet Pasricha & Song-Ping Zhu & Xin-Jiang He, 2022. "A closed-form pricing formula for European options in an illiquid asset market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-18, December.
    19. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Ma, Guiyuan & Siu, Chi Chung & Zhu, Song-Ping, 2019. "Dynamic portfolio choice with return predictability and transaction costs," European Journal of Operational Research, Elsevier, vol. 278(3), pages 976-988.
    21. Chaoqun Ma & Shengjie Yue & Hui Wu & Yong Ma, 2020. "Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 391-429, August.
    22. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    23. Taiga Saito & Akihiko Takahashi, 2017. "Derivatives Pricing with Market Impact and Limit Order Book," CARF F-Series CARF-F-385, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    24. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    25. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    26. Hu, Zhihao & Yang, Ben-Zhang & He, Xin-Jiang & Yue, Jia, 2024. "Equilibrium pricing of European crude oil options with stochastic behaviour and jump risks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 212-230.
    27. Huawei Niu & Dingcheng Wang, 2016. "Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1129-1145, July.
    28. Xie, Yurong & Deng, Guohe, 2022. "Vulnerable European option pricing in a Markov regime-switching Heston model with stochastic interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    29. Raheel Safdar & Mirza Sultan Sikandar & Tanveer Ahsan, 2019. "Market pricing of liquidity risk: evidence from China," China Finance Review International, Emerald Group Publishing Limited, vol. 9(4), pages 554-566, September.
    30. He, Xin-Jiang & Pasricha, Puneet & Lin, Sha, 2024. "Analytically pricing European options in dynamic markets: Incorporating liquidity variations and economic cycles," Economic Modelling, Elsevier, vol. 139(C).
    31. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    32. Yongmin Zhang & Shusheng Ding & Meryem Duygun, 2019. "Derivatives pricing with liquidity risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(11), pages 1471-1485, November.
    33. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    34. 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.
    35. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
    36. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(4), pages 519-529, December.
    37. Klein, Peter & Inglis, Michael, 2001. "Pricing vulnerable European options when the option's payoff can increase the risk of financial distress," Journal of Banking & Finance, Elsevier, vol. 25(5), pages 993-1012, May.
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