Asset Pricing Models with Stochastic Volatility

Abstract: Asset pricing modeling is a wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, three papers and appendices; we deal with asset pricing models with stochastic volatility. Here stochastic volatility modeling includes diffusion models and regime-switching models. Stochastic volatility models appear as a response to the weakness of the constant volatility models. In Paper A , we present a survey on popular diffusion models where the volatility is itself a random process and we present the techniques of pricing European options under each model. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. We consider Chiarella and Ziveyi model, which is a subclass of the model presented in Christoffersen and in paper A, we also explain a multi-factor stochastic volatility model presented in Chiarella and Ziveyi. We review the first-order asymptotic expansion method for determining European option price in such model. Multiscale stochastic volatilities models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. In paper B, we provide experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi. In paper C, we implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price di_erence criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coe_cient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model.