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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. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    3. Soren Bettels & Sojung Kim & Stefan Weber, 2022. "Multinomial Backtesting of Distortion Risk Measures," Papers 2201.06319, arXiv.org, revised Jan 2024.

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