This project implements a stochastic internal capital model using Monte Carlo simulation to estimate regulatory capital at a 99.5% Value-at-Risk (VaR) confidence level over a one-year horizon.
The model captures:
Underwriting Risk (frequency–severity framework)
Reserve Risk (development uncertainty)
Market Risk (equity and fixed income volatility)
Risk aggregation using Cholesky decomposition
Capital allocation via the Euler principle
Sensitivity and structural stress testing
Key Features
10,000+ Monte Carlo simulations (user adjustable)
Correlated risk aggregation
VaR and TVaR estimation
Parameter sensitivity engine (volatility, correlation, tail)
Dynamic stress scenarios (pandemic, inflation, catastrophe cluster, reinsurance failure)
Full capital allocation with marginal contribution validation
Interactive R Markdown (HTML output)
Methodology
Frequency: Poisson
Severity: Lognormal
Reserve risk: Normal / bootstrap approximation
Market risk: Normal / Student-t
Aggregation: Correlated simulation via Cholesky factorisation
Capital allocation:
VaR ] Allocated Capital i
=E[L i
∣L=VaR]
The model framework aligns conceptually with:
Solvency II internal model principles
Australian Prudential Regulation Authority ICAAP expectations
Enterprise risk management economic capital practices
Purpose
Designed as a demonstration of internal model architecture, enterprise capital modelling, and stochastic risk aggregation in R.
This model is intended for educational and internal analysis purposes only and does not represent a fully approved regulatory internal model.