Nonparametric option pricing under Beta-t-GARCH process with dynamic conditional score

Abstract

One of the advantages of nonparametric option pricing methods is that they only require a set of future price scenarios, eliminating the need for an explicit risk-neutral model for the price of the underlying asset. In this paper, we explore the score-driven Beta-t-GARCH volatility model, introduced by Harvey (2013), to generate the price scenarios necessary for a nonparametric option pricing method based on the empirical Esscher transform, as proposed by Pereira and Veiga (2017). An experiment was conducted using real data from the Brazilian Stock Market, comparing observed option prices across different strike prices and maturities with the prices produced by two variants of the proposed method and those produced by parametric models, specifically Black and Scholes (1973) and Heston and Nandi (2000). The results indicate that the combined approach of the Beta-t-GARCH model and the empirical Esscher transform show significantly better outcomes most of the time.