Valuation of Asian options with default risk under GARCH models

Abstract

In this paper, we consider Asian options with default risk under GARCH models. We adopt a GARCH process to describe the dynamics of the underlying asset and consider default risk in a reduced form model. In addition, the correlation between the intensity of default and the variance of the underlying asset is considered. In the proposed framework, we obtain closed-form pricing formulae of Asian options with/without default risk and show Asian option values in numerical examples. Specifically, the price of European (Asian) call options with default risk is not equal to the one of European (Asian) call options without default risk even when the initial value of the intensity equals zero.