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On the Pricing and Hedging of Volatility Derivatives

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  • Sam Howison
  • Avraam Rafailidis
  • Henrik Rasmussen
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    Abstract

    We consider the pricing of a range of volatility derivatives, including volatility and variance swaps. 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.

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    Bibliographic Info

    Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2003mf06.

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    Date of creation: 2003
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    Handle: RePEc:sbs:wpsefe:2003mf06

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