Modelling of and empirical studies on portfolio choice, option pricing, and credit risk

This thesis develops and applies a statistical spanning test for mean-coherent regular risk portfolios. Similarly in spirt to Huberman and Kandel (1987), this test can be implemented by means of a simple semi-parametric instrumental variable regression, where instruments have a direct link with a stochastic discount factor. Applications to different asset classes are studied. The results are compared to the conventional mean-variance approach. The second part of the thesis concerns option pricing under stochastic volatility and credit risk modelling. It is shown that modelling dynamics of the implied prices of volatility risk can improve out-of-sample option pricing performance. Finally, an equity-based structural model of credit risk with a constant elasticity of volatility assumption is discussed. This model might be particularly suitable for analysis of high yield fixed income instruments, where correlation between credit spreads and equity returns is substantial.

Essays on stochastic volatility and random-field models in finance.

In this thesis we develop random-field models for the implied volatility of equity options and the term structure of interest rates. Following a brief introduction to the topics of this thesis in chapter 1, chapter 2 models the Black-Scholes implied volatility of plain-vanilla European stock options as a random field with three parameters: current time, the maturity date and the exercise price of the corresponding option. In this model all plain-vanilla European options are needed to complete the market. Illiquid and exotic derivatives can be priced as a function of the stock price and the implied volatility surface. In chapter 3 we develop a random-field model for forward interest rates with stochastic volatility. It is assumed that the forward rate volatility function can be decomposed into a deterministic function of the time to maturity and a maturity- independent stochastic process driven by a standard Brownian motion. The separability of the forward-rate volatility function allows closed-form solutions to be obtained for the prices of a number of interest rate derivatives: bond options, interest rate caplets, and interest rate spread options. Forward LIBOR and swap rates are modelled in a similar way, and closed-form solutions are derived for the prices of LIBOR caplets and swaptions. In chapter 4 we estimate three random-field models of the term structure of interest rates: one model with deterministic forward-rate volatility, and two with stochastic forward-rate volatility. The models axe estimated using seven years of daily UK and US forward rate data, spanning times to maturity between zero and 120 months. The parameters of each model are obtained by maximizing the likelihood function. We develop an importance sampling technique that substantially reduces the variance of the Monte Carlo estimator of the likelihood function in the case of stochastic volatility