Empirická analýza modelů podmíněné volatility, šikmosti a kurtózy v oceňování opcí

Thesis aims to demonstrate the significant impact of volatility modeling on option pricing using the Black-Scholes equation, specifically its extension to the third and fourth moments as provided by Corrado and Su (1996). This extension adapts the Black-Scholes formula to account for non-normal skewness and kurtosis. The primary objectives are to apply GARCH models to capture time-varying conditional skewness and kurtosis, as discussed by León et al.(2005). These models were applied to daily returns of exchange rates to evaluate their effectiveness in capturing volatility dynamics. The impact of these models on option pricing was assessed by integrating them into the Black-Scholes framework for Forex options. The results indicate that specifications of time-varying skewness and kurtosis outperform those with constant third and fourth moments in terms of in-sample predictive power of conditional variances. Additionally, it was found that the modified Black-Scholes model outperforms the classical Black-Scholes model in out-of-sample performance. The significance of conditional skewness and kurtosis was also evident in option pricing, where the Black-Scholes models demonstrated improved pricing performance.