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Arbitrage Free Approximations to Candidate Volatility Surface Quotations

1
Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA
2
Department of Mathematics, KU Leuven, 3000 Leuven, Belgium
*
Authors to whom correspondence should be addressed.
J. Risk Financial Manag. 2019, 12(2), 69; https://doi.org/10.3390/jrfm12020069
Received: 19 February 2019 / Revised: 6 April 2019 / Accepted: 10 April 2019 / Published: 21 April 2019
(This article belongs to the Special Issue Option Pricing)
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Abstract

It is argued that the growth in the breadth of option strikes traded after the financial crisis of 2008 poses difficulties for the use of Fourier inversion methodologies in volatility surface calibration. Continuous time Markov chain approximations are proposed as an alternative. They are shown to be adequate, competitive, and stable though slow for the moment. Further research can be devoted to speed enhancements. The Markov chain approximation is general and not constrained to processes with independent increments. Calibrations are illustrated for data on 2695 options across 28 maturities for S P Y as at 8 February 2018. View Full-Text
Keywords: bilateral gamma; fast Fourier transform; sato process; matrix exponentials bilateral gamma; fast Fourier transform; sato process; matrix exponentials
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Madan, D.B.; Schoutens, W. Arbitrage Free Approximations to Candidate Volatility Surface Quotations. J. Risk Financial Manag. 2019, 12, 69.

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