In this thesis, the use of Levy processes to model the dynamics of Hedge fund indices is proposed. Merton (1976) and Kou (2002) models which differ on the specifcation of the jump components are employed to model hedge funds in continuous time. Secondly, an alternative to the Maximum Likelihood Estimation (MLE) method, Empirical Characteristic Function (ECF) estimation method, is explored in our analysis and compared to MLE. The Cumulant Matching Method (CMM) is used in getting the starting parameters; and the method that overcomes the major problem associated with this estimation method is outlined. Calibration shows that these two models t the data well, however, the empirical comparison shows that double exponential jumps are more consistent with the empirical data. Each fund's exposure to risk is calculated using Monte Carlo Value-at-Risk (VaR) estimation method.
A New Approach for Using Lévy Processes for Determining High-Frequency Value-at-Risk Predictions