A Comparison of Pricing Performance of GARCH Models with Alternative Leptokurtic Innovations for American Put Option
DOI:
https://doi.org/10.54097/fff9ms88Keywords:
Option pricing, GARCH models, Leptokurtic distributions, Generalized Error Distribution (GED), Student’s t distribution.Abstract
The Black-Scholes option pricing model assumes constant volatility, while the volatility smile observed in financial markets indicates that volatility is time-varying. This has motivated research on volatility modeling, among which Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are widely adopted. Leptokurtic innovation distributions are often employed to account for the excess kurtosis in asset returns. This paper compares the pricing performance of GARCH models with different innovation distributions, namely the Student’s t distribution and the Generalized Error Distribution. The volatility generated from AAPL stock prices over 2014-2018 by the GARCH models, along with historical volatility, is incorporated into the binomial tree to compute American put option prices. Empirical results show that the GARCH model with Generalized Error Distribution (GED) innovations outperforms that with Student’s t innovations, and both GARCH models outperform forecasts based on historical volatility. These findings provide evidence of a stronger pricing performance of GARCH models with GED innovation distribution compared to GARCH models with Student’s t distribution, and highlight the importance of leptokurtic distributions on GARCH-typed option pricing.
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