Vasicek Rate Model | Interactive Stochastic Simulation

An interactive web-based dashboard for exploring the Vasicek Interest Rate Model. This application performs real-time stochastic simulations, yield curve derivations, and probability forecasting entirely within the browser using PyScript.

Live Demo

---

Table of Contents

• Key Features
• Architecture
• The Mathematics
• Tech Stack
• Key Decisions
• Installation & Usage
• License

---

Key Features

1. Monte Carlo Simulation

Visualise hundreds of independent interest rate paths generated via Euler-Maruyama discretisation. The simulator accounts for mean reversion and volatility shocks in real-time.

2. Analytical Yield Curve

Derive the theoretical term structure for zero-coupon bonds based on the affine property of the Vasicek model.

3. Probability Distribution Forecasting

Calculate the statistical likelihood of rate outcomes at any future horizon using the Ornstein-Uhlenbeck transition density.

4. Interactive "Bento Box" Dashboard

A modern, glassmorphic UI that provides immediate feedback as model parameters are adjusted. Includes dynamic KaTeX typesetting for mathematical transparency.

---

Architecture

System Flow

The application follows a modular architecture where PyScript orchestrates the bridge between Pythonic scientific logic and JavaScript-driven visualisations.

graph TD
    A[index.html] -->|Initialises| B[PyScript Runtime]
    B -->|Orchestrates| C[main.py]
    C -->|Mathematical Logic| D[vasicek.py]
    C -->|Visualisation Config| E[charts.py]
    
    subgraph "Core Engine"
        D -->|Euler-Maruyama| F[SDE Solver]
        D -->|Analytical| G[Yield Curve Engine]
        D -->|Statistical| H[Distribution Calculator]
    end
    
    C -->|Render| I[Plotly.js Dashboard]

Loading

Directory Tree

vasicek-rate-model/
├── public/                 # Static assets and UI screenshots
├── charts.py               # Plotly chart configuration logic
├── index.html              # Main UI and application entry point
├── main.py                 # PyScript orchestration and event handling
├── pyscript.toml           # PyScript environment configuration
├── requirements.txt         # Python dependencies (NumPy, SciPy)
└── vasicek.py              # Core mathematical implementation

---

The Mathematics

The Vasicek model describes the evolution of interest rates as a Stochastic Differential Equation (SDE):

$$dr_t = a(b - r_t)dt + \sigma dW_t$$

• $a$ (Reversion Speed): The rate at which the process pulls back to the mean.
• $b$ (Long-Term Mean): The equilibrium interest rate level.
• $\sigma$ (Volatility): The magnitude of random market shocks.
• $dW_t$ (Wiener Process): Represents the stochastic component (Brownian Motion).

---

Tech Stack

Component	Technology
Runtime	PyScript (Pyodide)
Mathematics	NumPy, SciPy
Visualisation	Plotly.js
Typesetting	KaTeX
Styling	Vanilla CSS3 (Glassmorphism, Bento Grid)

---

Key Decisions

Decision	Rationale
Client-side Execution	Eliminates server costs and latency by running scientific simulations directly in the user's browser.
Vectorised Operations	NumPy is utilised to generate hundreds of simulation paths simultaneously, ensuring fluid UI updates.
Decoupled Logic	High-performance Python logic is separated from UI orchestration, allowing for easier auditing of the SDE implementation.

---

Installation & Usage

Prerequisites

• A modern web browser with WebAssembly support (Chrome, Firefox, Safari, Edge).
• A local web server for development.

Local Development

1. Clone the repository:

   git clone https://github.com/sahmed0/vasicek-rate-model.git

2. Navigate to the project directory:

   cd vasicek-rate-model

3. Start a local server (e.g., using Python):

   python -m http.server 8000

4. Open http://localhost:8000 in your browser.

---

License

This project is licensed under the GNU General Public License v3.0. See the LICENSE file for the full text.