Option valuation under GARCH models

Option pricing based on GARCH models is typically obtained under the assumption that the random innovations are standard normal (normal GARCH models). However, these models fail to capture the skewness and the leptokurtosis in financial data, so a number of various other distributions have been used. Since under GARCH models the market is incomplete, there are an infinite number of risk neutral measures for pricing contingent claims. The impact of the choice of an appropriate martingale measure on option pricing has yet to be addressed in these setups.; The present work investigates the applicability of some well-known risk neutral measures for various GARCH models. The most popular tool typically used for GARCH option pricing is the local risk neutral valuation relationship (LRNVR) introduced by Duan (1995) for normal GARCH models. In this framework we show that the same risk-neutralized dynamics are obtained when we apply a conditional Esscher transform, an Extended Girsanov principle, a discretized version of the Girsanov change of measure or a mean correcting martingale measure. However, when the normality assumption is violated these transformations are no longer consistent.