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Arbitrage-free approximation of call price surfaces and input data risk

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  • Judith Glaser
  • Pascal Heider

Abstract

In this paper we construct arbitrage-free call price surfaces from observed market data by locally constrained least squares approximations. The algorithm computes derivatives of the call surface accurately so that implied volatility, local volatility and transition probability density can be obtained at no additional cost. Observed input data are afflicted by a price uncertainty due to the bid--ask spread, quote imprecision and non-synchrony and cause an input data risk on the computed call surface and subsequently on the implied volatility surface. We model the input risk and perform an analysis to study and measure the effect of the input risk on the surfaces. With this analysis we can determine the trustworthiness of the computed results and their implications for option pricing a posteriori .

Suggested Citation

  • Judith Glaser & Pascal Heider, 2012. "Arbitrage-free approximation of call price surfaces and input data risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 61-73, August.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:1:p:61-73
    DOI: 10.1080/14697688.2010.514005
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    References listed on IDEAS

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    Cited by:

    1. Martin Tegn'er & Stephen Roberts, 2019. "A Probabilistic Approach to Nonparametric Local Volatility," Papers 1901.06021, arXiv.org, revised Jan 2019.
    2. Kai Yin & Anirban Mondal, 2023. "Bayesian uncertainty quantification of local volatility model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 290-324, May.
    3. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2022. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Papers 2207.02989, arXiv.org.
    4. Wang, Ximei & Zhao, Yanlong & Bao, Ying, 2019. "Arbitrage-free conditions for implied volatility surface by Delta," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 819-834.
    5. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2024. "A Semi-Closed Form Approximation of Arbitrage-Free Call Option Price Surface," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1431-1457, April.
    6. Miloš Kopa & Sebastiano Vitali & Tomáš Tichý & Radek Hendrych, 2017. "Implied volatility and state price density estimation: arbitrage analysis," Computational Management Science, Springer, vol. 14(4), pages 559-583, October.
    7. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    8. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2023. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Post-Print hal-03715921, HAL.
    9. Matúš Maciak & Sebastiano Vitali, 2024. "Using interpolated implied volatility for analysing exogenous market changes," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    10. repec:hal:wpaper:hal-03715921 is not listed on IDEAS
    11. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    12. Bender Christian & Thiel Matthias, 2020. "Arbitrage-free interpolation of call option prices," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 55-78, January.
    13. Tahar Ferhati, 2020. "Robust Calibration For SVI Model Arbitrage Free," Working Papers hal-02490029, HAL.
    14. Tahar Ferhati, 2020. "SVI Model Free Wings," Working Papers hal-02517572, HAL.
    15. Sebastiano Vitali & Miloš Kopa & Gabriele Giana, 2023. "Implied volatility smoothing at COVID-19 times," Computational Management Science, Springer, vol. 20(1), pages 1-42, December.

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