Comparison of asymmetric GARCH option pricing models using filtered historical simulations

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Title: Comparison of asymmetric GARCH option pricing models using filtered historical simulations
Author: Kurki, Kimmo
Contributor: University of Helsinki, Faculty of Social Sciences, Department of Economics
Date: 2009-12-07
Thesis level: master's thesis
Abstract: Option contracts are one of the most widely used financial covenants in today s financial markets. Generally, options are instruments that give the holder of an option a right, not obligation, to do something at a given time. Option pricing has received a great deal of attention after options became standard instruments for institutions and individuals to hedge against their financial risks. Option pricing theory has experienced a boom since the first developments in early 1970s. Various different techniques and approaches have been developed to predict option prices. The best known option pricing model is the Black-Scholes model which has an analytical, closed-form solution for the most common options. It has been shown that, despite its theoretical correctness, the Black-Scholes model fails to explain some well-documented biases in option markets, such as changing market volatility as well as underpricing of short maturity and deep out-of-the-money options. In this Thesis I study option pricing models, which are based on the time series model specifications. According to earlier option pricing literature, these models should be able to predict the option prices more accurately than the original Black-Scholes model, and they should also be able to model the market abnormalities more efficiently. Specifically, I use Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to predict option prices and compare the results from these models to an augmented Black-Scholes model that generalizes the original Black-Scholes model to use changing asset return volatilities. The GARCH pricing models are further augmented by Filtered Historical Simulation (FHS) method, which provides a technique for modeling the asymmetric return processes without making any definitive assumptions about the underlying return distribution. Option pricing models are applied to Standard & Poor 500 (S&P 500) index options that are the most actively traded equity options in the world. The S&P 500 index option are European style options that cover multiple strike prices and have maturities once each month, throughout the year. I find that GARCH-based option pricing models, that use FHS method, outperform more simple pricing models in stable market conditions. However, during more turbulent periods this relationship does not hold. I also find that GARCH based models can be used to model the generally acknowledged empirical observations in the option markets. GARCH models do not completely reduce the empirically observed underpricing biases, but they provide an effective tool to model changing return volatilities.
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