A note on the pricing and hedging of volatility
derivatives
Sam Howison, A. Rafailidis, H.O.
Rasmussen
Abstract
We consider the pricing of volatility products and
especially volatility and variance swaps. Under risk-neutral valuation we
provide closed form formulae for volatility-average and variance swaps. Also
we provide a general partial di erential equation for derivatives that have
an extra dependence on an av- erage of the volatility. We give approximate
solutions of this equation for volatility products written on assets for
which the volatility process uctuates on a timescale that is fast compared
with the lifetime of the contracts.
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