Quant Finance Foundations.
The bedrock — valuation, pricing, and the mathematics every model inherits.
8 articles · each one with a runnable notebook
Geometric Brownian Motion: Simulating Price Paths — Shown Through SPY
The canonical model for asset prices. We move from multiplicative returns to the GBM SDE and its closed-form solution, then calibrate to SPY and simulate a thousand five-year paths — checking the terminal distribution is log-normal and that zero drift makes it a martingale.
Black–Scholes & the Greeks
Five observable inputs in, a fair price and a full risk report out. We replicate the option, derive the Greeks in closed form, then price and risk-map a 3-month QQQ option from real data — and check it two ways: put-call parity and Monte Carlo.
Bond Pricing, Duration & Convexity: Via US Treasuries — and the ETFs That Lived Through 2022
Price, duration and convexity — the three numbers that summarise a bond's rate risk. We build them in 20 lines, walk the price-yield curve and the duration ladder, then check the theory against SHY/IEF/TLT's real drawdowns in the worst bond year in modern history.
Mean-Variance Optimization & the Efficient Frontier: A Six-Asset Portfolio in Python
Don't pick assets — pick the combination. We build the efficient frontier across six asset classes (2015–2024), see why every single ETF plots inside the cloud, and solve for the two portfolios everyone quotes: minimum variance and maximum Sharpe.
The Black-Litterman Model: Blending Market Equilibrium with Your Own Views
Reverse-optimize the market's implied returns, state one view — Germany at 10%, half confidence — and watch the Bayesian blend tilt the whole book sensibly while naive MVO lurches 75% into one country. Includes the no-views-equals-market sanity check.
Risk Parity from Scratch: Allocating by Risk, Not Capital — A Futures Portfolio
The 60/40 secret: capital weight ≠ risk weight. We compute marginal risk contributions across five futures, solve the risk-parity weights from scratch, match Riskfolio-lib to 1e-6, and scale the book to a 10% vol target with 1.45x leverage — the All-Weather mechanism in miniature.
Black–Scholes from First Principles: Deriving the Formula by Replication
No-arbitrage, a hedged portfolio, and a heat equation in disguise. We build Black–Scholes from the replication argument up, then implement the price and all five Greeks.
Gold Through War and Inflation: Twenty Years of GLD Against Real Yields
Gold is sold as an inflation and crisis hedge. We check the tape: its real driver is real yields, its inflation hedge is regime-dependent, and the geopolitical premium around conflict is real but fast-fading.