# Modeling and simulation of value -at -risk in the financial market area

Spring 2006

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Computational Analysis and Modeling

Raja Nassar

## Abstract

Value-at-Risk (VaR) is a statistical approach to measure market risk. It is widely used by banks, securities firms, commodity and energy merchants, and other trading organizations. The main focus of this research is measuring and analyzing market risk by modeling and simulation of Value-at-Risk for portfolios in the financial market area. The objectives are (1) predicting possible future loss for a financial portfolio from VaR measurement, and (2) identifying how the distributions of the risk factors affect the distribution of the portfolio. Results from (1) and (2) provide valuable information for portfolio optimization and risk management.

The model systems chosen for this study are multi-factor models that relate risk factors to the portfolio's value. Regression analysis techniques are applied to derive linear and quadratic multifactor models for the assets in the portfolio. Time series models, such as ARIMA and state-space, are used to forecast the risk factors of the portfolio. The Monte Carlo simulation process is developed to comprehensively simulate the risk factors according to the four major distributions used to describe data in the financial market. These distributions are: multivariate normal, multivariate t, multivariate skew-normal, and multivariate skew t. The distribution of the portfolio is characterized by combining the multifactor models with the Monte Carlo simulation process. Based on the characterization of the portfolio distribution, any VaR measure of the portfolio can be calculated.

The results of the modeling and simulation show that (1) a portfolio may not have the same kind of distribution as the risk factors if the relationship between the portfolio and the risk factors is expressed as a quadratic function; (2) the normal distribution underestimates risk if the real data have a heavy tail and a high peak; and (3) diversification is the best strategy of investment since it reduces the VaR by combining assets together.

The computational approach developed in this dissertation can be used for any VaR measurement in any area as long as the relationship between an asset and risk factors can be modeled and the joint distribution of risk factors can be characterized.

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