Lesson 5 of 8 · All lessons in this module
- The simulation framework: four steps, three sources of scenarios
- Historical simulation and historical VaR
- Historical simulation in practice: forecasts, data gaps and bonds
- Bootstrap resampling
- Bootstrapping in practice: price paths, confidence intervals and limits
- Monte Carlo simulation: what it is and what it is for
- Monte Carlo valuation with log returns: European and Asian options
- Correlated scenarios: Cholesky and multivariate Monte Carlo
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Lesson 5 of 8 · 14 min
Bootstrapping in practice: price paths, confidence intervals and limits
Bootstrapping turns a small historical sample into thousands of synthetic paths or resamples, letting you value payoffs and put confidence intervals on statistics without assuming a distribution.
In short
- Bootstrapping differs from historical simulation by drawing with replacement and treating the sample as a proxy for the population, not as the population itself.
- Every draw is independent: each observation has probability of being picked, whatever was drawn before.
- Log returns add up, so a bootstrapped terminal price is . Apply the payoff rule (e.g. ) to each path and summarise.
- A bootstrapped option value carries the sample's historical drift, so it need not match a risk-neutral, closed-form price.
- Bootstrapping a statistic (such as volatility) and taking percentiles of the results gives a confidence interval.
- Weaknesses: computationally intensive, only as good as the sample, breaks autocorrelation, cannot go beyond the observed range, gives no analytical insight.
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