Portfolio management, stochastic volatility and credit derivatives

: three important issues in quantitative finance

Abstract

During the financial crisis, most stock markets experienced large drawdown from the peak, volatilities in financial markets increased significantly, and the credit market became illiquid. This thesis consists of three parts which study three important topics related to the issues listed above. First, we propose a dynamic investment strategy which can do a good job to follow the market when the market soars, and can retain a part of the profit gained from the soaring market when the market experiences dramatic drawdown. We analyze the behavior of such an investment strategy and validate it by the empirical study. Secondly, we derive an analytic asymptotic formula for pricing European options in the fast mean-reverting stochastic volatility model. Approximations available in literatures failed to capture the behavior of the option prices when the current volatility is very large. Our new formula is in excellent agreement with the fully numerical solutions of option prices. Thirdly, we propose a pricing framework for credit derivatives in illiquid markets. In our framework, the default intensity, the position of the current portfolio, the trading size and the risk aversion of the investor are key inputs for pricing credit derivatives. One can determine a quote price for a trade at the current position, and determine the trading size for given market prices.

Date of Award	15 Feb 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Qiang ZHANG (Supervisor)