Pricing options using a score-driven model with jumps

Score-driven models can provide significant improvements over GARCH models in fitting and forecasting asset prices. We present a score-driven model with jumps (SDJ) for option pricing. In particular, the conditional variance of the returns is specified by an autoregressive process driven by the score of the predictive density, whereas jumps follow a compound Poisson process. This allows us to consider the interaction between jumps and volatility, as the Poisson process and the dynamics of the variance turn out to be fully coupled. Furthermore, we derive a sufficient condition ensuring ergodicity and strict stationarity of the return process. Finally, we generalize the SDJ to a bivariate model where the intensity of the Poisson process follows a score-driven autoregression too. We conduct both an in-sample and an out-of-sample analysis focusing on the times series of the options written on the S&P500. The results obtained reveal that our score-driven approaches with jumps provide a very satisfactory agreement with empirical data and outperform existing GARCH models with jumps. To the best of our knowledge, score-driven models have not been used for derivative pricing so far.