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European Option Pricing With Liquidity Shocks

Author

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  • MICHAEL LUDKOVSKI

    (Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA)

  • QUNYING SHEN

    (Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA)

Abstract

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled Hamilton–Jacobi–Bellman (HJB) equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. A comparative analysis between the model price and the classical Black–Scholes benchmark is given using the concepts of implied and adjusted time to maturity. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.

Suggested Citation

  • Michael Ludkovski & Qunying Shen, 2013. "European Option Pricing With Liquidity Shocks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-30.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:07:n:s021902491350043x
    DOI: 10.1142/S021902491350043X
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    References listed on IDEAS

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    1. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
    2. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
    3. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, June.
    4. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    5. Francis A. Longstaff, 2004. "Financial Claustrophobia: Asset Pricing in Illiquid Markets," NBER Working Papers 10411, National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Zhang, Hongyu & Guo, Xunxiang & Wang, Ke & Huang, Shoude, 2024. "The valuation of American options with the stochastic liquidity risk and jump risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    2. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    3. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing exchange options with stochastic liquidity and regime switching," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(5), pages 662-676, May.
    4. Li, Zhe & Zhang, Weiguo & Zhang, Yue & Yi, Zhigao, 2019. "An analytical approximation approach for pricing European options in a two-price economy," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    5. 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.
    6. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "Analytical valuation for geometric Asian options in illiquid markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 175-191.
    7. 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.
    8. 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).
    9. Tihomir Gyulov & Lyuben Valkov, 2015. "Well-Posedness and Comparison Principle for Option Pricing with Switching Liquidity," Papers 1502.07622, arXiv.org.

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