A risk calculation may require an expectation that has no convenient closed form. Simulation approximates that model expectation; resampling estimates uncertainty from observed data. This lesson uses the CLT to quantify Monte Carlo error and builds a percentile bootstrap interval for a mean return. It keeps simulation noise separate from model error and from uncertainty in the original sample.
Learning objectives. By the end of this note you should be able to:
- simulate continuous RVs by inverse transform and normals by standard generators;
- state the Monte Carlo estimator of an expectation and its CLT standard error;
- run the nonparametric bootstrap for a standard error and a percentile confidence interval;
- apply both tools to a terminal-wealth or mean-return problem with a fixed RNG seed.
In this lesson
- Simulation from a distribution
- Monte Carlo estimation and CLT error
- The bootstrap
Before you start
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