Market Risk Analysis Volume IV: Value-at-Risk Models

IV.4

Monte Carlo VaR

IV.4.1 INTRODUCTION

Monte Carlo simulation is an extremely flexible tool that has numerous applications to finance. It is often used as a method of ‘last resort’ when analytic solutions do not exist, or when other numerical methods fail. Its drawback has been the amount of time it takes to resolve a problem accurately using simulation, but as computers become more powerful this disadvantage becomes less relevant.

The purpose of this chapter is to provide a pedagogical introduction to Monte Carlo simulation with a specific focus on its applications to VaR estimation. There are two equally important design aspects of Monte Carlo VaR: the sampling algorithm and the model to which the algorithm is applied. Section IV.4.2 focuses on the first of these. It begins by explaining how pseudo-random numbers are generated. Then we introduce the sampling techniques that are based on low discrepancy sequences, which are commonly termed quasi Monte Carlo methods. The section then explains how to transform random numbers into simulations from a parametric distribution for risk factor returns, a process called structured Monte Carlo. Then we describe the technique of multi-step Monte Carlo, which is important for accounting for the dynamic properties of risk factor returns, such as volatility clustering.

The main aim of this chapter is to describe the different types of statistical models for risk factor returns that are used to underpin the simulation algorithm. A huge variety ...