The Mathematical Institute, University of Oxford, Eprints Archive

On the pricing and hedging of volatility derivatives

Howison, Sam and Rafailidis, Avraam and Rasmussen, Henrik (2003) On the pricing and hedging of volatility derivatives. Applied Mathematical Finance . (In Press)

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Abstract

We consider the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation we provide closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility. We describe a general partial differential equation framework for derivatives that have an extra dependence on an average of the volatility. We give approximate solutions of this equation for volatility products written on assets for which the volatility process fluctuates on a time-scale that is fast compared with the lifetime of the contracts, analysing both the ``outer'' region and, by matched asymptotic expansions, the ``inner'' boundary layer near expiry.

Item Type:Article
Uncontrolled Keywords:Volatility derivative
Subjects:A - C > Approximations and expansions
D - G > Game theory, mathematical finance, economics, social and behavioral sciences
Research Groups:Oxford Centre for Industrial and Applied Mathematics
Mathematical and Computational Finance Group
ID Code:100
Deposited By:Sam Howison
Deposited On:08 Jun 2004
Last Modified:20 Jul 2009 14:18

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