RESEARCH

ALL RESEARCH

Derivatives pricing, risk modeling, and stochastic calculus

Certificate in Quantitative Finance (CQF)

In Progress

Advanced 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 papers
quant

Advanced 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.

BSM closed form reproduces 10.4506 / 0.5323 (call / binary) to 4 decimals
Heston-Carr-Madan with Albrecher "little trap" — branch-cut-safe at long T
Monte Carlo VRF 2.9× European / 5.6× binary via strike-near-median antithetic effect
DerivativesHestonFourierMonte Carlo
quant

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.

Arithmetic & geometric Asian options with control-variate variance reduction
Barrier and lookback Monte Carlo with continuity correction
American-exercise pricing via Longstaff-Schwartz least-squares regression
ExoticsMonte CarloLongstaff-SchwartzPath-dependent
quant

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.

BSM PDE reduced to the heat equation and solved on a grid
Explicit, implicit, and Crank-Nicolson convergence side by side
CFL stability visualisation: watch explicit FDM blow up live
PDEFinite DifferenceCrank-NicolsonNumerical Methods
quant

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.

Garman-Kohlhagen FX option pricing with the two-rate skew
Vasicek and Hull-White short-rate yield-curve simulator
Merton structural model: equity as a call on firm value
FXRatesCreditVasicek
quant

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).

Per-asset Kupiec POF + Christoffersen independence VaR backtest
Stylized-facts diagnostic (CQF Module 2.4) on the live returns series
Gaussian vs Cornish-Fisher vs FHS comparison with recommended method per asset
VaRRiskBacktestingKupiec
quant

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.

Black-Scholes adaptation for non-standard underlying assets
Congestion risk modeling in deregulated electricity markets
Jump-diffusion and seasonality adjustments
DerivativesBlack-ScholesEnergy MarketsRisk Management

In Progress · Coming Soon

1 paper
quantComing Soon

Advanced 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.

Triple barrier labeling and meta-labeling
Sequential bootstrap and purged K-fold CV
Kelly criterion dynamic bet sizing
Quantitative FinanceMLPythonXGBoost