Three projects, built from first principles

Projects

Three tools built from first principles in Python, covering pricing, risk, and allocation. Each page goes through the math, the checks that show it works, and the code.

Move across the figure to set the spot price

01 · Derivatives pricing

Options pricing & volatility

Black-Scholes-Merton and binomial tree pricers, analytical Greeks, a PDE solver, and an implied volatility solver that turns a live options chain into a volatility surface.

contracts IV-solved: 3,800+
for the full SPY chain: < 4 s
expiries per surface: 32

BSM
CRR tree
Crank-Nicolson
Greeks
Newton-Raphson IV

Python
NumPy
SciPy
pandas
Streamlit
Plotly

Read the write-up

Re-runs between calm and crisis correlations

02 · Risk

Monte Carlo risk engine

Correlated return simulation through a hand-written Cholesky decomposition, VaR and CVaR, risk attribution by holding, correlation stress tests, and Kupiec backtesting.

Cholesky residual: 10⁻¹⁵
built-in checks: 5
dashboard tabs: 6

Cholesky
VaR / CVaR
Component VaR
Stress tests
Kupiec POF

Python
NumPy
SciPy
pandas
Streamlit
Plotly

Read the write-up

Move across the figure to pick a portfolio on the frontier

03 · Forecasting and allocation

Return forecasting & optimization

A Temporal Fusion Transformer forecasts five-day return quantiles, which feed mean-variance optimization with shrinkage covariance and a walk-forward backtest against simple benchmarks.

features per asset: 5
day forecast horizon: 5
dashboard tabs: 6

TFT
Quantile loss
Markowitz
Shrinkage
Walk-forward

Python
PyTorch
NumPy
SciPy
Streamlit
Plotly

Read the write-up