Estimating VaR: The Monte Carlo Simulation Method

Before Lehman Brothers closed during the global financial crisis, the global American-based bank had a large portfolio of lots of different types of assets and liabilities, so estimating the VaR for this portfolio would be quite the task! But that's where a Monte Carlo simulation would have been appropriate. Why do you think that's the case?

Exactly!

No. A trial and error method by hand would be so time consuming, the portfolio would change by the time you finished the simulation.

A Monte Carlo simulation would have been perfect for Lehman Brothers because it could have calculated the risks that were correlated together. That's because a Monte Carlo simulation allows the investor to input different assumptions about the statistical characteristics of the distribution of risk and use those characteristics to generate random outcomes that represent various returns.

The Monte Carlo simulation avoids the numerous steps of the parametric method, especially with a large portfolio, because it's not confined to a typical standard deviation. And in fact, a huge advantage of the Monte Carlo simulation is that it can run basically any distribution. What types of assets do you think would be best for a Monte Carlo simulation?

But there's one key step within the process that has a definitive impact on the Monte Carlo outcomes: the number of random values that the simulation is asked to generate. Just think about how a larger number of random values will impact the outcomes of the Monte Carlo simulation. What's the impact?

No, actually. More random values would make the simulation process longer, not shorter.

That's not it. More values do impact the simulation.

Bingo! The Monte Carlo simulation would be more accurate as the number of random values increases because more outcomes would be produced, and those outcomes would increase the probability that the simulation will capture the future outcome. Once you've decided how many random values to generate, you can then sort the outcomes from worst to best and look for the certain percentile you specify.

Exactly! Options have various distribution scenarios, so the Monte Carlo simulation is the best approach to capture that kind of risk. That means that the Monte Carlo simulation could run thousands of different scenarios and produce a wide range of possibilities. Then it's simply ordering the statistical outcomes into a worst- to best-case scenario.

That's not it. Bonds have a pretty standard distribution.

Not quite. While the Monte Carlo simulation would work for an equity position, its real benefit can be found with other assets.

Typically this result will be pretty close to the parametric VaR model, with the difference coming from the parametric assuming certain parameters, but the Monte Carlo simulation actually samples a population with those parameters. And just like the historical simulation method, you can scale the returns to run an estimated VaR.

To summarize: [[summary]]

Monte Carlo simulations use a computer to generate an estimate of VaR

Monte Carlo simulations use a by-hand trial and error method to approximate the estimate of VaR

Bonds

Equities

Options

It's less time consuming

The outcomes are more reliable

It doesn't impact the Monte Carlo simulation

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