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Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility

Author

Listed:
  • H. Yin

    (Minnesota State University Mankato
    Graduate University of Chinese Academy of Sciences)

  • Y. Wang

    (Peking University)

  • L. Qi

    (Hong Kong Polytechnic University)

Abstract

The interpolation of the market implied volatility function from several observations of option prices is often required in financial practice and empirical study. However, the results from existing interpolation methods may not satisfy the property that the European call option price function is monotonically decreasing and convex with respect to the strike price. In this paper, a modified convex interpolation method (with and without smoothing) is developed to approximate the option price function while explicitly incorporating the shape restrictions. The method is optimal for minimizing the distance between the implied risk-neutral density function and a prior density function, which allows us to benefit from nonparametric methodology and empirical experience. Numerical performance shows that the method is accurate and robust. Whether or not the sample satisfies the convexity and decreasing constraints, the method always works.

Suggested Citation

  • H. Yin & Y. Wang & L. Qi, 2009. "Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 243-266, July.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:1:d:10.1007_s10957-009-9541-4
    DOI: 10.1007/s10957-009-9541-4
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    References listed on IDEAS

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    Cited by:

    1. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    2. Gianluca Cassese, 2015. "Non Parametric Estimates of Option Prices Using Superhedging," Papers 1502.03978, arXiv.org.
    3. Xavier Bay & Laurence Grammont & Hassan Maatouk, 2017. "A new method for interpolating in a convex subset of a Hilbert space," Computational Optimization and Applications, Springer, vol. 68(1), pages 95-120, September.

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