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Calibrating a Diffusion Pricing Model with Uncertain Volatility: Regularization and Stability

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  • DOMINICK SAMPERI

Abstract

A regularized (smoothed) version of the model calibration method of Avellaneda, Friedman, Holmes, and Samperi (1997) is studied. We prove that the regularized formulation is solvable and that the solution depends continuously on the input data (observed derivative security prices). Associated issues of model credibility, stability, and robustness (insensitivity to model assumptions) are discussed. The Implicit Function Theorem for Banach spaces is used for the stability proof, and some numerical illustrations are included.

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  • Dominick Samperi, 2002. "Calibrating a Diffusion Pricing Model with Uncertain Volatility: Regularization and Stability," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 71-87, January.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:1:p:71-87
    DOI: 10.1111/1467-9965.00005
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    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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    Cited by:

    1. Dai, Min & Tang, Ling & Yue, Xingye, 2016. "Calibration of stochastic volatility models: A Tikhonov regularization approach," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 66-81.
    2. Stephane Crepey, 2004. "Delta-hedging vega risk?," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 559-579.
    3. Stavros J. Sioutis, 2017. "Calibration and Filtering of Exponential L\'evy Option Pricing Models," Papers 1705.04780, arXiv.org.

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