A good model for the description of stock prices and its instantaneous volatility is crucial for the assessment of risk, for portfolio optimization and for option pricing. Mathematical models require different properties depending on its usage. However, no matter how rich the class of models is, if parameter values cannot be estimated, their applicability is limited. Barndoff-Nielsen and Shephard describe an important affine stochastic volatility model for the logarithm of stock prices in which the randomly changing volatility is expressed by a Lévy driven Ornstein-Uhlenbeck (OU) process. This leads to an unknown closed form of the density and therefore a direct application of maximum likelihood estimation is not possible. The aim of this thesis was the development of an alternative estimator based on the joint characteristic function (JCF) since this estimation method requires no tractable form of the likelihood function but contains the same amount of information. We developed a general form of the JCF and the corresponding estimator for the BN-S model with Gamma-OU volatility process. Moreover we discussed the asymptotic properties of this estimator and derived the corresponding asymptotic variance of this JCF estimator. We also provide a simple moments estimator which gives acceptable starting values for the minimization and analyzed the approach on simulated data.     «

A good model for the description of stock prices and its instantaneous volatility is crucial for the assessment of risk, for portfolio optimization and for option pricing. Mathematical models require different properties depending on its usage. However, no matter how rich the class of models is, if parameter values cannot be estimated, their applicability is limited. Barndoff-Nielsen and Shephard describe an important affine stochastic volatility model for the logarithm of stock prices in which...     »