An Introduction to Value-At-Risk, Fourth Edition

Chapter 6

MONTE CARLO SIMULATION AND VALUE-AT-RISK

A defining characteristic of options is their non-linear pay-off profile. This makes risk exposure estimation for an options portfolio more problematic compared with a portfolio comprised of linear pay-off profile instruments such as bonds, futures and swaps. For this reason practitioners frequently eschew the variance– covariance methodology in favour of what is called the Monte Carlo simulation approach, because it is believed to provide a more accu-rate estimation of risk exposure for option instruments. MonteCarlo simulation refers to a process whereby a series of prices for an asset (or assets) is generated by a computer program; these prices are all theoretically possible given certain user-specified parameters. The portfolio is then revalued at each of these possible prices, and this enables the user to calculate a VaR number for the portfolio.

In this chapter we introduce the Monte Carlo simulation method and its use as a value-at-risk (VaR) calculation methodology.

INTRODUCTION: MONTE CARLO SIMULATION

We first consider the concept of simulated prices and their application to option valuation.

Option value under Monte Carlo

Table 6.1 reprises our European option contract from Chapter 5. Note an additional parameter, the ‘drift’. This reflects what is known as the stochastic nature of asset price movements as defined in the ...