Skills: Python. Numerical Methods. Visualisation Libraries. Stochastic Calculus. Statistical Analysis.  Financial Modelling and Computing. Numerical Optimisation. Statistical and Risk Analysis.

How should weights be assigned to assets in a portfolio? This project explores the question by numerically maximising an objective function, which could be one of (1) the Sharpe Ratio, (2) Markowitz Mean-Variance, or (3) the negative Variance of a given portfolio with any number of assets using gradient ascent. Optional modifications to these ratios are also implemented to avoid overfitting, which includes penalty for overconcentration (concentration measured by HHI) and a risk tolerance parameter. These modifications can be toggled on or off.  A plotting option is also available for three asset portfolios to visualise the maximisation, which visualises the optimisation process as picking the highest point on the objective surface. (Jan 2025, Year 2) 

Skills: Python. Numerical Methods. Visualisation Libraries. Stochastic Calculus. Statistical and Risk Analysis. Financial Modelling and Computing. Web Design. 

Developed a web application that generates the expected volatility and return distribution for user-defined portfolios, enabling easy access to VaR and cVaR, as well as additional statistics of returns and volatility, such as standard deviations and multiple averages for risk management. The dynamics of price and volatility was captured with the Heston stochastic volatility model, which was simulated via Monte Carlo with a user-defined number of paths. Each price path of the Monte Carlo simulation was numerically solved using the Quadratic-Exponential Scheme proposed by Andersen (2008). Parameters of the Heston model were estimated using statistical methods, with historical closing price data sourced from Yahoo Finance over a user-defined period of time. (Dec 2025, Year 2) 

Skills: Python. Numerical Methods. Visualisation Libraries. Stochastic Calculus. Financial Modelling and Computing.

Is there a way to  accurately predict stocks?  Turns out, the answer is not reliably - even if you have all the right parameters (which is already unlikely). In this project, a realistic model of the market is simulated through numerically solving the Black-Scholes stochastic model. Volatility and drift are accurately modelled with the Heston model to reflect real world effects such as volatility clustering and mean reversion. (Dec 2024, Year 1)