Quantitative Risk Engine: Monte Carlo Portfolio Simulation

This repository contains a high-performance Python risk engine that evaluates the financial risk of a multi-asset portfolio using Monte Carlo simulations. The project maps correlated financial assets into a stochastic process to calculate institutional risk metrics, including Value at Risk (VaR) and Conditional Value at Risk (CVaR).

Mathematical Foundation

The simulation models asset paths using Geometric Brownian Motion (GBM). The continuous-time stochastic differential equation (SDE) is defined as:

$$ dS_t = \mu S_t dt + \sigma S_t dW_t $$

Where:

• $S_t$ = Asset price at time $t$
• $\mu$ = Expected drift (annualized return)
• $\sigma$ = Asset volatility
• $dW_t$ = A Wiener process (Standard Brownian Motion)

Modeling Correlated Assets (SciPy Matrix Decompositions)

In real-world markets, asset movements are not independent. To accurately simulate this, the engine relies on the SciPy library (scipy.linalg.cholesky) to perform a Cholesky Decomposition on the portfolio's correlation matrix $C$.

By calculating the lower triangular matrix $L$ (where $C = L L^T$), we successfully transform uncorrelated standard normal random shocks into correlated shocks, thereby mapping real-world macro-market relationships into the stochastic diffusion component.

Software Architecture

To prioritize execution speed and scalability, the simulation circumvents the need for slower, lower-level languages (like C++) by utilizing NumPy's vectorized operations. The Monte Carlo engine runs 10,000 parallel portfolio simulations spanning 252 trading steps in fractions of a second.

• src/gbm_simulator.py: Object-Oriented simulation engine housing the linear algebra routines and SDE calculations.
• src/risk_metrics.py: Isolated logic for calculating statistical percentiles and expected shortfalls.
• main.py: Entry point for configuring the mock portfolio and generating matplotlib visualizations.

Getting Started

1. Clone the repository.

git clone [https://github.com/josephquigley01-cmd/Quantitative-Risk-Engine.git](https://github.com/josephquigley01-cmd/Quantitative-Risk-Engine.git)
cd Time-Series-Anomaly-Detection-for-Predictive-Maintenance

2. Install dependencies:

pip install -r requirements.txt

3. Run main.py

python main.py