A FINITE DIFFERENCE METHOD FOR THE VALUATION OF VARIANCE SWAPS

Thomas Little and Vijay Pant
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Thomas Little: Deutsche Bank AG, 31 West 52nd Street New York, NY 10019, USA
Vijay Pant: PricewaterhouseCoopers, 1177 Avenue of the Americas, New York, NY 10036, USA

Chapter 12 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume III), 2002, pp 275-295 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe develop here a finite difference approach for valuing a discretely sampled variance swap within a Black-Scholes framework. This approach incorporates the observed volatility skew and is capable of handling various definitions of the variance. It is benchmarked against Monte-Carlo simulation in the presence of a volatility skew and is shown to provide extremely accurate values for a variance swap. Our method is based on decomposing the problem of valuing a variance swap into a set of one-dimensional PDE problems, each of which is then solved using a finite difference method.

Keywords: Quantitative Analysis; Financial Markets (search for similar items in EconPapers)
Date: 2002
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