ALL RESEARCH
Derivatives pricing, risk modeling, and stochastic calculus
Certificate in Quantitative Finance (CQF)
In ProgressAdvanced program covering derivatives pricing, risk management, stochastic calculus, numerical methods, and machine learning in finance. Each paper below traces back to a specific Module 3 lecture.
Built & Live
6 papersAdvanced Option Pricing Models
An interactive pricing studio covering Black-Scholes-Merton, Heston stochastic volatility (via the Carr-Madan Fourier transform), and Monte Carlo simulation with antithetic variates. Live Greeks surfaces, 3D implied-volatility skew, and a companion review paper synthesising CQF Module 3.
Exotic Options Lab
Where the Black-Scholes closed form runs out. This page prices Asian, barrier, lookback, and American-exercise options under GBM using Monte Carlo path-dependence and the Longstaff-Schwartz regression. Includes live path-explorer animations and a copy-pasteable Python pricer.
Finite Difference Solver
Solving the Black-Scholes PDE directly on a grid. Explicit, implicit, and Crank-Nicolson schemes side by side, with a live stability visualisation showing exactly when the explicit method blows up past the CFL bound, and projected SOR for American early exercise.
Pricing Where GBM Breaks
A catalogue of markets where lognormal equity assumptions fail and the models that replace them: Garman-Kohlhagen for FX with two interest rates, Vasicek and Hull-White for rates, the Merton structural model for credit, and the Schwartz mean-reverting model for commodities.
Commodity Risk Lab
Live VaR backtesting (Kupiec POF + Christoffersen independence), stylized-facts diagnostics, and side-by-side Gaussian / Cornish-Fisher / Filtered Historical Simulation method comparison on six commodity tickers. Data pipeline: Supabase + daily GitHub Actions ETL.
Financial Transmission Rights Pricing
Most option pricing models assume the underlying is a stock or a commodity. This paper takes the Black-Scholes framework and adapts it for Financial Transmission Rights, where the underlying is congestion risk on a power grid. Includes jump-diffusion models, seasonality adjustments, and interactive LMP charts.
In Progress · Coming Soon
1 paperAdvanced ML Trading System
Implementation of methods from Lopez de Prado's Advances in Financial Machine Learning. CUSUM filters for event detection, triple barrier labeling, meta-labeling for signal confidence, purged K-fold cross-validation, and Kelly criterion for position sizing. Built in Python with XGBoost.