VALUE AT RISK MODELS

Applications of Value-at-Risk Models for Risk Management

[Name of the Institute]Table of Contents

CHAPTER 1 INTRODUCTION3

Background3

Defining VAR4

A Short History of VaR4

Problem Statement6

Research Aims and Objectives6

CHAPTER 2 LITERATURE REVIEW8

The Development of VAR10

Case Study Example- Procter & Gamble12

CHAPTER 3 RESEARCH METHODOLOGY14

Analytical VaR14

Historical Simulation Approach15

CHAPTER 1 INTRODUCTION

Background

The dissertation is devoted to study of risk management techniques for decision making in highly uncertain environments. The traditional framework of decision making under the presence of uncertainties relies on stochastic programming (Birge and Louveaux, 1997; Pr´ekopa, 1995) or simulation (Ripley, 1987) approaches to surpass simpler quasi-deterministic techniques, where the uncertainty is modeled by relevant statistics of the stochastic parameters, such as expectation or variance. One method of limiting an institution's risks in derivatives trading is to place a limit on the amount it can lose with a given probability over a specified period of time. For instance, one might consider the losses at a 1% level over ten days or at a 5% level over one day. This value is called Value-at-Risk or VAR.

Often a financial institution's portfolio consists of many underlying instruments, such as equities, fixed-income securities, commodities and so on. All these instruments depend hundreds of market variable, and many different types of risk measures are produced daily to capture the performance of portfolio. However, this does not give the senior manager much better understanding of the current performance of the portfolio or the portfolio value forecast under the volatile future market conditions. Hence, the value at risk (VaR) measure is soon introduced, which compresses the Greek letters for all market variables into one single number and makes comparison between performances of different portfolios much simpler.

Defining VAR

In its most general form, the Value at Risk measures the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval. Thus, if the VaR on an asset is $ 100 million at a one-week, 95% confidence level, there is a only a 5% chance that the value of the asset will drop more than $ 100 million over any given week. In its adapted form, the measure is sometimes defined more narrowly as the possible loss in value from “normal market risk” as opposed to all risk, requiring that we draw distinctions between normal and abnormal risk as well as between market and nonmarket risk.

While Value at Risk can be used by any entity to measure its risk exposure, it is used most often by commercial and investment banks to capture the potential loss in value of their traded portfolios from adverse market movements over a specified period; this can then be compared to their available capital and cash reserves to ensure that the losses can be covered without putting the firms at risk.

A Short History of VaR

While the term “Value at Risk” was not widely used prior to the mid 1990s, the origins of the measure lay further back in time. The mathematics that underlies VaR was largely developed in the context of portfolio ...