No abstract

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on SP 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

This paper provides simple, analytic approximations for pricing exchange‐traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite‐difference, binomial, or compound‐option pricing methods.

We propose filtering historical simulation by GARCH processes to model the future distribution of assets and swap values. Options' price changes are computed by full reevaluation on the changing prices of underlying assets. Our methodology takes implicitly into account assets' correlations without restricting their values over time or computing them explicitly. VaR values for portfolios of derivative securities are obtained without linearising them. Historical simulation assigns equal probability to past returns, neglecting current market conditions. Our methodology is a refinement of historical simulation.

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on SP 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.