Implementation of the Euler-Maruyama method for solving stochastic differential equations

This project provides a comprehensive numerical analysis of the Brusselator model, a theoretical framework for autocatalytic chemical reactions. The implementation spans deterministic solvers, stochastic differential equations (SDEs), and Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC).

Fullstack Bates (1996) Option Pricing Engine: A high-performance engine utilising Inverse Fourier Transforms for real-time calibration and Euler-Maruyama Monte Carlo for path projections. Optimised for 2026-2027 market volatility regimes and jump-diffusion dynamics.

End-to-End Python implementation of consistent intergenerational pension optimization from Alonso-Garcia et al. (2026). Solves optimal PAYG pension policy via forward CRRA utilities and closed-form HJB feedback laws. Features a 10,000-path Euler-Maruyama Monte Carlo engine, Cholesky-correlated 4D Brownian shocks, and demographic stress-testing.

A production-grade stochastic interest rate modeling engine that calibrates the Vasicek model to historical SOFR data using OLS regression and Euler-Maruyama simulation.

Benchmarking framework for forecasting stochastic differential equations. 5 SDEs (GBM, CIR, Heston, OU, Double-Well) × 7 models (ARIMA through TCN and Transformer). Full paper with results and derivations.

Analytical and computational analysis of modeling the motion of self-propelled microswimmers in 2-D.

This project is an interactive quantitative finance dashboard that models interest rate term structures using the Vasicek Short-Rate Model.

This software solves a coupled stochastic differential Equation to simuate the timing noise in neutron stars

Simulação da taxa de juros com o modelo CIR (Euler–Maruyama e Milstein), Monte Carlo para precificação de bonds e construção da curva a termo.