C++ Exotic Option Pricing Engine

🚀 Overview

A high-performance Monte Carlo simulation engine designed to price Path-Dependent Exotic Options (specifically Down-and-Out Barrier Call Options).

Unlike standard Black-Scholes implementations that assume a static time-step ($T$), this engine utilizes Geometric Brownian Motion (GBM) to discretize the simulation into daily trading steps ($dt = 1/252$), allowing for rigorous barrier monitoring and volatility analysis.

⚡ Key Features

• Path Dependency: Simulates 252 discrete time-steps per path to enforce barrier conditions.
• Stochastic Accuracy: Utilizes std::mt19937 (Mersenne Twister) for high-fidelity normal distribution generation, avoiding the biases of rand().
• Latency Optimization: Implements "Early Exit" logic; paths that breach the barrier are terminated immediately, reducing CPU cycles by ~30% in high-volatility scenarios.
• Drift/Diffusion Pre-calculation: Mathematical constants are computed outside the hot loops to minimize redundant FLOPs.
• Data Serialization: Exports simulation paths to .csv for downstream analysis in Python (Pandas/Matplotlib).

🧮 Mathematical Model

The asset price trajectories are modeled using the discrete form of Geometric Brownian Motion:

$$S_{t+\Delta t} = S_t \cdot \exp \left( (r - \frac{1}{2}\sigma^2)\Delta t + \sigma \sqrt{\Delta t} Z \right)$$

Where:

• $S_t$: Stock Price at time $t$
• $r$: Risk-free interest rate
• $\sigma$: Volatility
• $Z$: Standard Normal Random Variable $\sim N(0,1)$

🛠️ Performance Metrics

• Simulations: 100,000 Paths
• Steps per Path: 252 (Total ~25.2 Million Steps)
• Execution Time: ~1.74 seconds (on standard hardware)
• Throughput: ~57,000 simulations/second

💻 Build & Run

Dependencies: Standard C++ Library (STL) only. No external dependencies required.

# Compile using g++ with optimization flags
g++ -O3 -o option_pricer main.cpp

# Run the executable
./engine


Starting Simulation for AAPL...
--------------------------------
Theoretical Option Price: 10.425
Time Taken: 1.74484 seconds
Simulations per Second: 57312
Data saved to 'simulation_data.csv'