Financial Risk Management

CHAPTER 9A Brief Overview of Monte Carlo Simulation

Among many other potential applications, Monte Carlo simulation can be used to generate a collection of random market risk factor scenarios.¹ Considering our Google/Amazon portfolio, the market risk factor is defined as the return of each stock. Indeed, any decreases in daily stock prices will generate a negative return and thus a loss in value. This holds true for the Profit and Loss (P&L).

The general idea of Monte Carlo simulation is to generate market risk factors from a theoretical probability distribution (think about the Gaussian model) while preserving the correlation between asset returns in the portfolio. Ideally, the selected theoretical distribution should not be too far from the assets or portfolio observed/historical distributions. The “garbage in, garbage out” rule also applies here.

The Monte Carlo methodology consists of three major steps:

1. Scenario generation. Using the volatility and correlation estimates for the assets in the portfolio (Google and Amazon), we produce n simulations of market risk factors (returns) in accordance with a theoretical probability distribution (unsurprisingly, the Gaussian framework is the easiest to use).
2. Portfolio valuation. For each scenario, we compute a simulated value of the portfolio value.
3. Risk measure. We then compute a quantile for a given confidence level to compute the Value‐at‐Risk (VaR).

In conclusion, the Monte Carlo method is simply another way to simulate market ...