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Arbitrage Free Approximations to Candidate Volatility Surface Quotations

Dilip B. Madan () and Wim Schoutens ()
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Dilip B. Madan: Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA
Wim Schoutens: Department of Mathematics, KU Leuven, 3000 Leuven, Belgium

Journal of Risk and Financial Management, 2019, vol. 12, issue 2, 1-21

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.

Keywords: bilateral gamma; fast Fourier transform; sato process; matrix exponentials (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2019
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