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Nonparametric Option Pricing with No-Arbitrage Constraints

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  • Melanie Birke
  • Kay F. Pilz

Abstract

We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating the state price density for an underlying asset price from its option prices. It can be shown that the call price estimator is pointwise consistent and asymptotically normal. The estimator of the state price density is also consistent. In a simulation study we compare the new estimators to the estimators given in Aït-Sahalia and Duarte (2003). Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

Suggested Citation

  • Melanie Birke & Kay F. Pilz, 2009. "Nonparametric Option Pricing with No-Arbitrage Constraints," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 53-76, Spring.
    • Handle: RePEc:oup:jfinec:v:7:y:2009:i:2:p:53-76
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbn016
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    Citations

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    Cited by:

    1. Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    2. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    3. Taboga, Marco, 2016. "Option-implied probability distributions: How reliable? How jagged?," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 453-469.
    4. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2019. "Option Implied Risk-Neutral Density Estimation: A Robust and Flexible Method," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 705-728, August.
    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. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    7. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    8. 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.
    9. Liu, Xiaoquan & Cao, Yi & Ma, Chenghu & Shen, Liya, 2019. "Wavelet-based option pricing: An empirical study," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1132-1142.
    10. Guidolin, Massimo & Wang, Kai, 2023. "The empirical performance of option implied volatility surface-driven optimal portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    11. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.

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