Pricing variance, gamma, and corridor swaps using multinomial trees

This article introduces a new methodology to approximate the prices of variance, gamma, and corridor swaps in a stochastic volatility framework applicable to any given tree structure. The efficiency of this tree method is based on decomposing the payoff structure into nested conditional expectations, which may be calculated using a single pass through the tree. The total number of calculations is commensurable with the number of tree nodes, making it substantially faster than Monte Carlo simulations. We exemplify the methodology using two different tree structures that approximate several types of stochastic volatility models. Furthermore, this methodology is general enough to be applied to any given tree structure. Extensive numerical tests show that the methodology introduced is fast, efficient, and accurate. The method was applied to volatility instruments quoted on the CBOE.