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 Suite
Derivatives pricing engine I built for CQF Module 3 (Exam 2, April 2026). Implements Black-Scholes-Merton, Heston stochastic volatility (priced via the Carr-Madan Fourier inversion), and Monte Carlo with antithetic variates. Reproduces the BSM closed-form to four decimals; measures a 2.9× variance reduction on the European call and 5.6× on the binary.
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
Applied CQF Module 2.3 risk-machinery (Kupiec POF + Christoffersen independence + combined conditional coverage) to live commodity returns. Built on the daily Supabase pipeline I maintain for Muda Coffee — six tickers, fresh data nightly via GitHub Actions. Each asset gets its own thesis-driven VaR method recommendation; the Cornish-Fisher backtest on KC clears all three tests at the 95% level (p = 0.664 / 0.697 / 0.843).
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.