A GARCH Option Pricing Model with Filtered Historical Simulation

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.

The pricing kernel puzzle: survey and outlook

“…Last, Barone-Adesi, Engle, and Mancini (2008) cannot find the pricing kernel puzzle in three years' worth of S&P 500 data (2002)(2003)(2004) using essentially the methodology of Rosenberg and Engle (2002). However, Barone-Adesi, Mancini, and Shefrin (2013) essentially repeat the study and come to the conclusion, that the pricing kernel puzzle is indeed present in the data.…”

Structural GARCH: The Volatility-Leverage Connection

“…Our Monte Carlo approach is motivated by option models estimated when the underlying follows a GARCH type process, as in Barone-Adesi, Engle, and Mancini (2008). When pricing options on GARCH processes, there is often no closed form solution for call prices, necessitating the use of simulation techniques.…”

The Pricing Kernel Puzzle in Forward Looking Data

“…Instead, we allow both unrestricted pricing kernels and ones, which are restricted to monotonically decrease. Second, Barone-Adesi, Engle, and Mancini (2008) and Barone-Adesi and Dall'O (2010) argue that their 1 See e.g. Cochrane (2000), pp.…”