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On the calibration of distortion risk measures to bid-ask prices

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  • Karl F. Bann�r
  • Matthias Scherer

Abstract

We investigate the calibration of a non-linear pricing model to quoted bid-ask prices and show the existence of a solution in a broad class of distortion risk measures, following the frameworks of Cherny and Madan [ Int. J. Theor. Appl. Financ. , 2010, 13 (8), 1149-1177] and Bann�r and Scherer [ Eur. Actuarial J. , 2013, 3 (1), 97-132]. We present an approximation of distortion risk measures by a piecewise linear approximation of concave distortions. This is used to construct a tractable non-parametric calibration procedure to bid-ask prices based on piecewise linear concave distortion functions. To analyze the specific structure of distortion functions, we calibrate quoted bid-ask prices non-parametrically and w.r.t. parametric families and obtain a jump-linear structure. Hence, we suggest considering the parametric family of -expectation convex combinations as a possible family of distortion functions. This family allows fast and efficient calibration and has an appealing economic interpretation.

Suggested Citation

  • Karl F. Bann�r & Matthias Scherer, 2014. "On the calibration of distortion risk measures to bid-ask prices," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1217-1228, July.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:7:p:1217-1228
    DOI: 10.1080/14697688.2014.887220
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    3. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    6. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
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    Cited by:

    1. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586, arXiv.org, revised Mar 2016.
    2. Soren Bettels & Stefan Weber, 2024. "An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models," Papers 2408.02401, arXiv.org.
    3. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    4. 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).
    5. Soren Bettels & Sojung Kim & Stefan Weber, 2022. "Multinomial Backtesting of Distortion Risk Measures," Papers 2201.06319, arXiv.org, revised Aug 2024.

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