VaR/ES risk engine

A risk engine that estimates Value at Risk and Expected Shortfall on a portfolio under six different models, then backtests each one against realized returns to see which tail estimate actually holds up.

Models compared

• Delta-normal — the fast, closed-form baseline. Assumes returns are Gaussian, which understates tail risk.
• Historical simulation — resamples actual past returns; makes no distributional assumption, but treats yesterday’s volatility as today’s.
• Multivariate-$t$ Monte Carlo — simulates from a fitted multivariate Student-$t$, capturing fat tails and cross-asset dependence.
• GARCH-filtered historical simulation (GARCH-FHS) — rescales standardized historical residuals by today’s forecast volatility $\sigma_{t+1}$, so the tail reacts to current conditions instead of the whole sample window.
• EVT with GPD tails — fits a Generalized Pareto Distribution to exceedances above a threshold, for quantiles beyond what the sample can see directly.
• Marchenko–Pastur covariance cleaning — denoises the sample correlation matrix before it feeds the Monte Carlo engine, so the simulation isn’t trusting eigenvector directions that are pure noise.

Backtesting

Each model is scored with Kupiec’s POF test for VaR coverage and a joint VaR–ES scoring function, since $\ES_\alpha$ isn’t elicitable on its own. The live simulation on the homepage runs the GARCH-FHS path forward in real time.