A NEW REPRESENTATION OF THE LOCAL VOLATILITY SURFACE

Marianito R. Rodrigo () and Rogemar S. Mamon
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Marianito R. Rodrigo: Department of Mathematics, Instituto Tecnológico Autónomo de México, Rio Hondo #1, Col. Tizapan San Angel, Mexico City, Mexico 01000, Mexico
Rogemar S. Mamon: Department of Statistical and Actuarial Sciences, University of Western Ontario, Canada, 1151 Richmond Street, London, Ontario, Canada N6A 5B7, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 07, 691-703

Abstract: In this paper, we address the problem of recovering the local volatility surface from option prices consistent with observed market data. We revisit the implied volatility problem and derive an explicit formula for the implied volatility together with bounds for the call price and its derivative with respect to the strike price. The analysis of the implied volatility problem leads to the development of an ansatz approach, which is employed to obtain a semi-explicit solution of Dupire's forward equation. This solution, in turn, gives rise to a new expression for the volatility surface in terms of the price of a European call or put. We provide numerical simulations to demonstrate the robustness of our technique and its capability of accurately reproducing the volatility function.

Keywords: Implied volatility; Dupire's equation; inverse problem; ansatz approach; nonlinear system (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0219024908004993

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