PhD Candidate in Mathematics at the University of Kent, specialising in computational finance and topological modelling. I develop high-performance C++ models for option pricing (Black-Scholes, Heston) and LSTM neural networks for stock price prediction, optimised with OpenMP and SIMD. Explore my projects below or at github.com/rhesus1/Finance.
I am a PhD candidate at the University of Kent, with a thesis on Abelian Higgs vortex dynamics, implemented in C++ with OpenMP optimisation. My expertise in quantitative finance includes option pricing (Black-Scholes, Heston), algorithmic trading, and portfolio optimisation, developed through professional courses and projects in Python and C++. I have implemented LSTM neural networks for stock price prediction and optimised PDE solvers for financial modelling, bridging theoretical insights with practical applications in risk management and trading systems.
Education: PhD in Mathematics (2021–2025, viva pending), MSc Mathematics (First Class Honours, 2020–2021), BSc Mathematics (First Class Honours, 2017–2020), University of Kent.
This visualisation showcases a Long Short-Term Memory (LSTM) neural network developed in C++ to predict Amazon stock prices. The plot below compares predicted prices against actual market data, highlighting the model’s potential for financial forecasting and algorithmic trading. Data was fetched via curl and parsed with nlohmann/json, achieving a 5% RMSE improvement over baseline models. See code at github.com/rhesus1/Finance/LSTM.
Explore my computational work in quantitative finance. The visualisations below, computed using C++ with SIMD and OpenMP optimisations (30% speedup), include option pricing models for Amazon using Black-Scholes (Analytical, Finite Difference, Monte Carlo) and Heston (Fourier, Monte Carlo, Finite Difference) methods. See code at github.com/rhesus1/Finance/OptionPricing.
This 3D plot visualises call option prices as a function of strike price and time to maturity, computed using the Heston model’s Fourier method.
This 3D plot shows the implied/local volatility surface, highlighting the Heston model’s stochastic volatility dynamics.
These plots compare call and put option prices across Black-Scholes (Analytical, Finite Difference, Monte Carlo) and Heston (Fourier, Monte Carlo, Finite Difference) models for a range of strike prices. We see that the three methods for Black-Scholes all agree.
This 1x3 grid of scatter plots compares call option prices for Amazon across Market, Black-Scholes, and Heston models, categorized by moneyness (ATM: |strike - spot| < 5; OTM: 20 < strike - spot < 30; ITM: 10 < strike - spot < 20). Prices are plotted against time to expiry, with Market (black stars), Black-Scholes (blue crosses), and Heston (red triangles) models, computed using C++ with numerical optimizations.
This 1x3 grid of scatter plots compares put option prices for Amazon across Market, Black-Scholes, and Heston models, categorized by moneyness (ATM: |strike - spot| < 5; OTM: -30 < strike - spot < -20; ITM: -20 < strike - spot < -10). Prices are plotted against time to expiry, with Market (black stars), Black-Scholes (blue crosses), and Heston (red triangles) models, computed using C++ with numerical optimizations.
My PhD research focuses on Abelian Higgs vortex dynamics, implemented in C++ with finite difference methods and OpenMP parallelisation, directly applicable to financial PDE solvers (e.g., Black-Scholes, Heston). Below are simulations from my publications.
This video showcases a computational simulation of excited Abelian Higgs vortices, illustrating their dynamic behaviour as studied in my PhD research on vortex dynamics.
This video showcases a computational simulation of excited Abelian Higgs vortices, showcasing the formation of a spectral wall for vortices oscillating out of phase.
Download my CV for details on my academic and professional background.
Download CV (PDF)I’m eager to apply my C++ and quantitative finance expertise to innovative trading systems. Let’s connect!
Email: reesjmorgan@gmail.com
LinkedIn: morgan-rees-8a5008288
GitHub: rhesus1
Google Scholar: Morgan Rees