Monte Carlo simulation

Category: Risk identification & assessment · Reviewed by Amy Price, Account Executive · Last reviewed

Monte Carlo simulation

Monte Carlo simulation is a computational technique that estimates the distribution of an outcome by repeatedly sampling input variables from their underlying probability distributions and evaluating the model for each sample. Named after the Monaco casino district, it was developed by Stanislaw Ulam and John von Neumann on the Manhattan Project in the 1940s.

Application to insurance

Monte Carlo is the dominant numerical technique for:

• Capital modelling — projecting the distribution of insurer surplus under Solvency II internal models.
• Aggregate claims modelling — combining a claim-frequency distribution (e.g. Poisson, negative binomial) with a claim-severity distribution (e.g. lognormal, Pareto) to produce an aggregate loss distribution.
• Reinsurance structure pricing — valuing layers, aggregate deductibles, reinstatements.
• Catastrophe modelling — outputs of RMS, AIR and Verisk models are stochastic event sets evaluated by simulation.
• Asset-liability modelling — projecting investment returns alongside claim payments.

Key concepts

• Convergence — accuracy improves with √n; doubling precision requires four times the simulations.
• Variance reduction — Latin Hypercube, antithetic variates, importance sampling reduce simulations needed.
• Tail metrics — Value at Risk (VaR) and Tail Value at Risk (TVaR) are read from the simulated tail.
• Correlation — dependency between input variables is modelled via copulas (Gaussian, t, Clayton, Gumbel).

Regulatory anchor

Under Solvency II (Directive 2009/138/EC, Article 101), the Solvency Capital Requirement is calibrated to the 99.5% one-year Value at Risk. Internal models almost universally use Monte Carlo to evidence this.

References

• IEC 31010:2019, Annex B.32.
• IFoA (various). Risk and capital management — practical guides.
• Solvency II Directive 2009/138/EC, Article 101.

Cross-references

• Probabilistic risk assessment
• Quantitative risk assessment
• Internal model Solvency II
• Catastrophe model

Maintained by Matt Bartlett, Director, Apex Insurance Brokers Limited. FCA FRN 724952. Companies House 07014570.