Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
A finite-difference method for the valuation of variance swaps
Thomas Little, Vijay Pant
Abstract
ABSTRACT
We develop here a finite-difference approach for valuing a discretely sampled variance swap within an extended 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.
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