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Discrete-time option pricing with stochastic liquidity

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  • Leippold, Markus
  • Schärer, Steven

Abstract

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant 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

  • Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    • Handle: RePEc:eee:jbfina:v:75:y:2017:i:c:p:1-16
    DOI: 10.1016/j.jbankfin.2016.11.014
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    Cited by:

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    6. 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.
    7. 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).
    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 & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo CIEF 15923, Universidad EAFIT.
    10. 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.
    11. 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.
    12. 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.
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    More about this item

    Keywords

    Market liquidity; Bid-Ask spreads; Option pricing; Stochastic liquidity; Conic finance;
    All these 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

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