FRTB Market Risk Engine

A self-contained, educational implementation of a market-risk capital engine built around the four pillars of the Basel Fundamental Review of the Trading Book (FRTB) Internal Models Approach (IMA). It measures market risk with Value at Risk (VaR) and Expected Shortfall (ES), validates the model using the full regulatory backtesting suite, calibrates a stressed-period capital number, and runs a P&L Attribution Test (PLAT).

The project deliberately uses a simple rolling-window historical-simulation model to expose a central insight of FRTB: a risk model can appear well‑calibrated on average, pass naive frequency tests, and earn a regulatory "green light", yet still fail the more sophisticated timing‑aware and tail‑sensitive tests — under‑protecting exactly when protection matters most.

---

What the project does

The engine works with a three‑asset portfolio containing genuinely different risk behaviours: an equity ETF (SPY), a long‑Treasury ETF (TLT), and gold (GLD), weighted 50 / 30 / 20. It pulls real market data via yfinance and automatically falls back to a synthetic, correlated, fat‑tailed return generator (with two embedded crisis windows) if the download fails or returns too little data.

The code is organised around four pillars:

1. Measurement – VaR and ES engine
   One‑day‑ahead rolling VaR and ES via historical simulation (no distributional assumptions). VaR is the empirical quantile of the trailing loss window; ES is the mean of losses beyond that quantile. FRTB mandates ES at 97.5% confidence; VaR is also reported at 99%.

2. Backtesting – proving the model is statistically accurate
   A complete validation suite:

   • Basel Traffic Light test (green / yellow / red zones), both full‑period and rolling 250‑day.
   • Kupiec Proportion‑of‑Failures test (unconditional coverage).
   • Christoffersen Independence test (detects clustering of exceptions).
   • Christoffersen Conditional Coverage (frequency + independence combined).
   • Acerbi–Szekely Z1 and Z2 statistics for backtesting Expected Shortfall, with Monte‑Carlo p‑values.
   • Berkowitz density‑forecast tail test.
   • Bootstrap confidence intervals for risk statistics such as ES.

3. Stressed‑window calibration
   Slides a 250‑day window across the full history, selects the one that maximises ES, and reports the stress multiplier (stressed ES ÷ current ES). The worst window is labelled against a list of known historical crises (e.g. COVID‑19, the 2022 rate‑hike rout).

4. P&L Attribution Test (PLAT)
   Compares the model’s theoretical (sensitivity‑based) P&L with the desk’s actual P&L using Spearman rank correlation and an unexplained‑variance ratio, then assigns a green / amber / red zone.

Finally, main() runs all four phases end to end, prints a formatted daily market‑risk report, and saves two diagnostic charts (breaches.png and breach_intensity.png).

---

Requirements

• Python 3.8+ (developed on 3.11)
• numpy – numerical arrays and vectorised rolling‑window computations
• pandas – time‑series handling
• scipy – statistical distributions and tests (chi‑squared, Spearman, normal quantiles)
• yfinance – downloading real market data (optional at runtime; the engine falls back to synthetic data when unavailable)
• matplotlib – diagnostic plots
• A Jupyter environment (jupyterlab or notebook) to open and run the .ipynb

---

Installation

Clone the repository and (recommended) create a virtual environment:

git clone https://github.com/jennied2/FRTB-Market-Risk-Engine.git
cd FRTB-Market-Risk-Engine