Since the seminal work of Black and Scholes [1973] and Merton [1973], their option pricing formula has in spite of some well-documented systematic pricing biases been used in trading rooms throughout the world. The heteroscedasticity of asset returns in particular has developed into an important area of research. The most popular option pricing model which accommodates for a changing volatility over time is the continuous-time stochastic volatility model developed by Heston [1993]. Since continuous-time stochastic volatility models are difficult to implement and test, discrete-time GARCH option pricing models, which allow an easy estimation of the current volatility from historical asset prices observed at discrete-time intervals, are studied in detail in this thesis. Further advantages of GARCH option pricing models are examined, which include the fact that the variance of the spot asset follows a stochastic GARCH process, that the model possesses a leptokurtic and, if needed, skewed distribution, and that the correlation between returns of the spot asset and its volatility as well as volatility clustering is captured by the model. As a result, GARCH option pricing models are able to explain the skewed implied volatility surface associated with the Black/Scholes Model. The risk-neutral valuation of the option price in a GARCH framework is considerably more complicated and, therefore, a generalized version of risk-neutralization, called LRNVR, is used. The GARCH option pricing model by Duan [1995] and further developed versions are analyzed. Then, the closed form GARCH option pricing model by Heston and Nandi [2000] is examined and closed form formulas for the most important Greeks are derived. Resulting pricing and hedging differences compared to the Black/Scholes Model are analyzed, from which the conclusion can be drawn that the GARCH option pricing model is a substantial improvement compared to the Black/Scholes Model. Furthermore, it is shown that discrete-time GARCH option pricing models possess a continuous-time diffusion limit.      «

Since the seminal work of Black and Scholes [1973] and Merton [1973], their option pricing formula has in spite of some well-documented systematic pricing biases been used in trading rooms throughout the world. The heteroscedasticity of asset returns in particular has developed into an important area of research. The most popular option pricing model which accommodates for a changing volatility over time is the continuous-time stochastic volatility model developed by Heston [1993]. Since continu...     »