Monte Carlo Model Validation
Validating Monte Carlo requires testing the path generator, convergence to benchmarks, and confidence-interval coverage.
Explanation
The path generator is checked by comparing simulated moments and distributions with theoretical targets at selected time points.
Prices for products with analytical or semi-analytical solutions are used as benchmarks for convergence studies across path counts.
Confidence intervals based on estimated standard errors should contain benchmark prices with frequencies close to their nominal levels.
Fixed seeds and common random numbers can turn Monte Carlo tests into reproducible diagnostics instead of fragile random experiments.
monte carlovalidationconvergenceconfidence intervals
Interactive visualisation
Monte Carlo model validation
Validate paths, convergence to benchmarks, and CI coverage.
S
100
K
100
r
0.020
vol
0.25
T
1.00
Monte Carlo run
paths
5000
seed
11
Coverage test
trials
40
Benchmark (Black–Scholes)
10.87056
MC estimate ± z·SE
11.18134 ± 0.49888
1) Path generator momentsCHECK
Compare sample mean/variance of S(T) to theoretical GBM targets.
E[S(T)] theo
102.0201
sample: 102.0255
rel err: 0.0001
Var[S(T)] theo
671.27
sample: 636.22
rel err: 0.0522
2) Convergence to benchmark
3) CI coverage
Observed coverage
83% (33/40)
Expected: around 95% if SEs are correct and the generator is sound.
Interpretation
- First validate the generator (moments/distributions). Otherwise convergence is meaningless.
- Then validate convergence against products with known benchmarks.
- Coverage checks whether your uncertainty estimates are honest.