IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1615.html

Discrete-Time Option Pricing with Stochastic Liquidity

Author

Listed:
  • Markus Leippold

    (University of Zurich - Department of Banking and Finance; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute; University of Zurich - Faculty of Economics, Business Administration and Information Technology)

  • Steven Schaerer

    (University of Zurich, Students)

Abstract

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to signi ficant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500.

Suggested Citation

  • Markus Leippold & Steven Schaerer, 2016. "Discrete-Time Option Pricing with Stochastic Liquidity," Swiss Finance Institute Research Paper Series 16-15, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1615
    as

    Download full text from publisher

    File URL: http://ssrn.com/abstract=2744493
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. is not listed on IDEAS
    2. He, Xin-Jiang & Wei, Wenting & Lin, Sha, 2025. "A closed-form formula for pricing exchange options with regime switching stochastic volatility and stochastic liquidity," International Review of Financial Analysis, Elsevier, vol. 103(C).
    3. 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.
    4. Lucio Fiorin & Wim Schoutens, 2020. "Conic quantization: stochastic volatility and market implied liquidity," Quantitative Finance, Taylor & Francis Journals, vol. 20(4), pages 531-542, April.
    5. Xin‐Jiang He & Hang Chen & Sha Lin, 2025. "A Closed‐Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(5), pages 429-440, May.
    6. 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).
    7. Alghalith, Moawia, 2020. "Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Moawia Alghalith & Wing-Keung Wong, 2022. "Option Pricing Under an Abnormal Economy: using the Square Root of the Brownian Motion," Advances in Decision Sciences, Asia University, Taiwan, vol. 26(Special), pages 4-18, December.
    9. Lina M. Cortés & Javier Perote & Andr�s Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo de Valor Público 15923, Universidad EAFIT.
    10. Lin, Sha & Chen, Meiling & He, Xin-Jiang, 2025. "Analytically pricing crude oil options under a jump-diffusion model with stochastic liquidity risk and convenience yield," The North American Journal of Economics and Finance, Elsevier, vol. 78(C).
    11. Ziming Dong & Dan Tang & Xingchun Wang, 2023. "Pricing vulnerable basket spread options with liquidity risk," Review of Derivatives Research, Springer, vol. 26(1), pages 23-50, April.
    12. 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.
    13. 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.
    14. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    15. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    16. 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).
    17. 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.
    18. 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.
    19. Gao, Rui & Li, Yaqiong & Lin, Lisha, 2019. "Bayesian statistical inference for European options with stock liquidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 312-322.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:chf:rpseri:rp1615. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    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.