Beyond Black-Scholes: A Computational Framework for Option Pricing Using Heston, GARCH, and Jump Diffusion Models

Battle Count: 122

Highly relevant to quantitative trading as it directly addresses derivatives pricing, which is fundamental to options trading strategies, hedging, and risk management. The framework provides practical tools for pricing options under realistic market conditions (stochastic volatility, jumps, time-varying volatility). The comparison across models helps traders select appropriate pricing models for different market regimes. However, it focuses on European options and does not address execution, market microstructure, or real-time trading considerations.

Moderate complexity. The Monte Carlo simulation and GBM are straightforward. GARCH(1,1) implementation is simplified via the Python 'arch' package. The Heston model requires simulating correlated Brownian motions and calibrating three parameters (kappa, theta, sigma_v). The Merton Jump-Diffusion adds Poisson process simulation. L-BFGS-B optimization is standard. The main complexity lies in correctly implementing the stochastic differential equations, ensuring proper discretization, and calibrating multiple models simultaneously. Python with standard financial libraries makes this accessible to intermediate-level quantitative developers.

The paper provides detailed algorithms (4 algorithms), parameter settings (10,000 simulations, 100 time steps, interest rate 0.047), and specifies Python with Yahoo Finance API and arch package. However, no GitHub repository is provided, no exact random seeds are mentioned, and the L-BFGS-B optimizer implementation details are partially described. The use of live market data from November 2024 makes exact reproduction difficult. Stock selection (TSLA, META, AMC, MARA, SHOP) is clearly defined.