Statistics Seminar: Hobson -- Robust hedging of variance swaps

David Hobson
Department of Statistics
University of Warwick, UK

Location: Carslaw 273

Time:  2pm Friday, March 30, 2012

Title: Robust hedging of variance swaps

Abstract: 
Consider the problem of pricing the floating leg of variance swap. Under
the twin assumptions of continuous monitoring and a price process which is
continuous, Dupire and Neuberger separately showed how the variance swap
can be replicated perfectly with an investment in the underlying and the
puchase of -2 (minus two) log contracts. The log contracts can be
replicated with vanilla options so that if calls and puts are liquidly
traded then the variance swap has a unique model independent price.

But what if the price process is not continuous, or if, as is always the
case in practice, the payoff of the variance swap is based on price
changes over a finite number of dates?

We show how to construct best possible sub- and super-hedges for the
variance swaps, and describe the worst case models. A perhaps suprising
corollary is that the effects of jumps depends crucially on the precise
formulation of the kernel of the variance swap.