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Implied liquidity: Model sensitivity

Author

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  • Albrecher, Hansjoerg
  • Guillaume, Florence
  • Schoutens, Wim

Abstract

The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity λ of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the λ, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post-crisis under a wide range of models and to study implied liquidity time series which could give an insight for future stochastic liquidity modeling. In particular, we perform a maximum likelihood estimation of the CIR, Vasicek and CEV mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility as the liquidity process reverts much faster to its long-run mean. Moreover, a comparison of the parameter estimates between the pre- and post-credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods.

Suggested Citation

  • Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    • Handle: RePEc:eee:empfin:v:23:y:2013:i:c:p:48-67
    DOI: 10.1016/j.jempfin.2013.05.003
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Guillaume, F., 2015. "The LIX: A model-independent liquidity index," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 214-231.
    2. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    3. Yerli, Cigdem & Eksi-Altay, Zehra & Selcuk-Kestel, A. Sevtap, 2023. "On the information content of implied liquidity measure: Evidence from the S&P 500 index options," Finance Research Letters, Elsevier, vol. 57(C).
    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. Florence Guillaume & Gero Junike & Peter Leoni & Wim Schoutens, 2019. "Implied liquidity risk premia in option markets," Annals of Finance, Springer, vol. 15(2), pages 233-246, June.
    6. Chuang, Ming-Che & Tsai, Jeffrey Tzuhao, 2024. "Determining bid-ask prices for options with stochastic illiquidity and applications to index options," Pacific-Basin Finance Journal, Elsevier, vol. 84(C).
    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. Sun, Xianming & Gan, Siqing & Vanmaele, Michèle, 2015. "Analytical approximation for distorted expectations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 246-252.
    9. 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.
    10. 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.
    11. 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.

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    More about this item

    Keywords

    Implied liquidity; Conic finance; Model sensitivity; Pre-and post-crisis liquidity;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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