A Study on Value-at-Risk and Lévy Processes

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.

Download Full-text

Estimation of Multivariate Asset Models with Jumps

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109018001321 ◽

2018 ◽

Vol 54 (5) ◽

pp. 2053-2083 ◽

Cited By ~ 1

Author(s):

Laura Ballotta ◽

Gianluca Fusai ◽

Angela Loregian ◽

M. Fabricio Perez

Keyword(s):

At Risk ◽

Risk Management ◽

Value At Risk ◽

Levy Processes ◽

Finite Sample ◽

Computationally Efficient ◽

Efficiency Gains ◽

Finite Sample Properties ◽

Non Gaussian ◽

Empirical Illustration

We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets because it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail in an empirical illustration.

Download Full-text

Modelling Hedge Fund Indices Using Levy Processes

10.32920/ryerson.14654616 ◽

2021 ◽

Author(s):

Ugochi T. Emenogu

Keyword(s):

Hedge Funds ◽

Value At Risk ◽

Lévy Processes ◽

Hedge Fund ◽

Estimation Method ◽

Likelihood Estimation ◽

Levy Processes ◽

Empirical Characteristic Function ◽

Empirical Comparison ◽

Double Exponential

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.

Download Full-text