ROUGH MARKED HESTON-HAWKES MODEL: SIMULATION AND ANALYSIS

This project develops and implements a GPU-accelerated simulation framework for a rough marked Heston-Hawkes using PyTorch. The model couples a Rough Heston process for asset price and volatility dynamics with a marked Hawkes process that generates events with implied volatility marks. The IV marks are sampled from a density estimated via GPU-accelerated kernel density estimation on historical SPY options data. A Finite Difference scheme is employed for the simulation, with key components, including correlated noise generation, a simplified fractional Brownian motion (FBM) increment approximation, and Hawkes intensity calculation, implemented using PyTorch tensors for GPU acceleration. The simulation generates multiple paths of asset price, variance, and marked event streams. The results are analyzed and visualized, comparing simulated IVs and event features to the original data distributions and qualitatively assessing the simulated paths. Performance optimization efforts, including vectorizing the kernel sum calculation, are evaluated. The study highlights the feasibility of using GPU acceleration for simulating complex jump-diffusion and point processes and discusses limitations and areas for future research, such as improving FBM simulation accuracy and implementing conditional mark sampling.