On the pricing and hedging of volatility derivatives |
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Authors: | Sam Howison Avraam Rafailidis Henrik Rasmussen |
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Affiliation: | 1. Mathematical Institute University of Oxford 24-29 St. Giles OX1 3LB Oxford UK howison@maths.ox.ac.uk henrik.rasmussen@orange.net;2. Department of Mathematics King's College London Strand, London WC2R 2LS UK avraam@mth.kcl.ac.uk |
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Abstract: | The paper considers the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility are provided. A general partial differential equation framework for derivatives that have an extra dependence on an average of the volatility is described. Approximate solutions of this equation are given for volatility products written on assets for which the volatility process fluctuates on a timescale 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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