THE VARIANCE SWAP CONTRACT UNDER THE CEV PROCESS

Abstract

The problem of pricing the variance swap when the underlying asset follows the CEV process is considered. A hedging argument is used to replicate the variance swap in part using the log contract. The price of the log contract is shown in practice to provide a fast and accurate pricing method for the variance swap. An exact integral solution to the log contract price is derived along with simple exact and approximate formulas. Asymptotic methods are used to obtain the approximations. The situation when default is possible under the CEV process is considered. The shifted CEV model is introduced as an alternative if default can occur and asymptotic pricing formulas are constructed. The applicability and accuracy of the results are demonstrated numerically for the log contract and hence the variance swap.