Valuation of volatility derivatives as an inverse problem

Peter Friz and Jim Gatheral

Quantitative Finance, 2005, vol. 5, issue 6, 531-542

Abstract: Ground-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps and calls on variance. The latter leads to an ill-posed problem that we solve using regularization techniques. The sum is divergent, that means we can do something Heaviside†

Date: 2005
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DOI: 10.1080/14697680500362452

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