Corridor Variance Swaps

It is widely recognised that delta-hedged positions in options can be used to trade volatility. To facilitate volatility trading for their clients, several institutions routinely offer variance swaps. A variance swap is a financial contract that upon expiry pays the difference between a standard historical estimate of daily return variance and a fixed rate determined at inception. As in any swap, the fixed rate is initially chosen so that a variance swap has zero cost to enter. See Demeterfi et al (1999) or Carr & Madan (1998) for pricing and Chriss & Morokoff (1999) for risk management issues. Over the past few years, several institutions have also begun offering corridor variance swaps. These differ from standard variance swaps only in that the underlying’s price must be inside a specified corridor in order for its squared return to be included in the floating part of the variance swap payout. As in a standard variance swap, the fixed payment is made at maturity and is initially chosen so that the corridor variance swap has zero cost to enter. In the corridor variance swap considered in this chapter, the fixed payment is independent of the occupation time of the corridor. However, variations exist in which the fixed payment accrues over time at a constant rate only while the underlying is in the corridor. A corridor variance swap is a generalisation of a standard variance swap in that the latter results from the former when the corridor is extended to all possible price levels. An upside variance swap uses a corridor extending from a fixed barrier up to infinity, while a downside variance swap uses a corridor extending from a fixed barrier down to zero. From the speculator’s perspective, the 1