Accurate pricing and hedging of equity variance swaps

Quant Talk
Wednesday, 12 May 2010
6.30 pm, room 21

No registration necessary. Just turn up and enjoy!

Abstract

Under the assumption that a stock follows a diffusion process with a deterministic short rate, an equity variance swap can be perfectly replicated with a static portfolio of vanilla options as well as a simple delta hedging strategy in the stock. The robustness of this replication, as well as the fact that variance swaps provide a convenient means for trading volatility, have contributed to it becoming a widely used product. Consequently, bid/ask spreads for variance swaps on major underlyings can be quite tight and, in some situations, the classic pricing and replication method alone is no longer adequate. Practitioners are well aware of this and commonly apply a number of corrections to the classic variance swap price. In this talk we present corrections for dealing with stochastic interest rates, discrete dividends and over(under)-hedging using a finite number of vanilla options. Next, we consider products where the daily accumulated variance is subject to a spot dependent weighting function, such as corridor variance swaps or gamma swaps. Similarly to the simple variance swap, a quasi-static hedge can be constructed under weak assumptions for the underlying diffusion. In general, this theoretical hedge will involve European options maturing at all intermediate times up to the expiry of the weighted variance swap, and thus in practice one must approximate it with a finite number of option maturities. We propose a method for selecting these maturities, and the associated vanilla option weights, that results in a very good approximation, and that allows us to over (under)-hedge the weighted variance swap.