Monte Carlo method

Monte Carlo methods in VaR analysis

In Value at Risk analysis, an alternative method for calculating the probability distribution (rather than using the Delta-normal method or the Historical simulation method).

Monte Carlo simulations consist of two steps:

First, a stochastic (random) process for financial variables is specified as well as process parameters.

Both historical data and appropriate judgement can be used for such parameters as risk and correlations.

Second, multiple fictitious price paths are simulated for all variables of interest. At each horizon considered, the portfolio is marked-to-market using full valuation.

A distribution of returns is eventually produced, from which a VaR figure can be measured.

Comparing the methods:

1. The Delta-normal method is the simplest method to implement.

The main drawbacks are the assumption that risk factors have normal distributions, and the assumption that the assets are linear (in other words, that they do not contain options).

2. The Historical simulation method is also relatively simple to implement.

The main drawback is that the historical information used may not adequately represent future probability distributions. (This is also a drawback of the delta-normal method.)

Monte Carlo techniques are designed to address these shortcomings.

Disadvantages of Monte Carlo methods include their relative complexity.

Monte Carlo methods in other applications

More generally, Monte Carlo methods are the simulation of multiple fictitious outcomes, using a combination of historical and judgemental parameters and a randomised process.

The name originated from the famous Monte Carlo casino.

See also

• Delta-normal method
• Historical simulation method
• Stochastic
• Value at risk