Option pricing under GARCH models with Hansen's skewed-t distributed innovations

Recently, there has been a wave of work on option pricing under GARCH-type models with non-normal innovations. However, many of the existing valuation results rely on the existence of the moment generating function of the innovations’ distribution, thereby ruling out the use of heavy-tailed distributions such as Student's t and its variants, which may better capture the excess kurtosis in historical asset returns. In this paper, we consider option pricing under GARCH models with Hansen's skewed-t distributed innovations. To overcome the limitations of the existing valuation results, we apply risk-neutralization to the empirical distribution of the simulated sample paths rather than the innovations’ parametric distribution. We illustrate our proposed method by pricing options written on the S&P 500 index.