Options pricing and quant finance, worked through
Each post takes one concept — Black-Scholes, a Greek, a portfolio idea — and works through the math and a real Python snippet, the way we’d explain it to a strong high schooler who knows pre-calc. Not a textbook restatement.
The Black-Scholes Formula, Explained From Scratch
What each term in the Black-Scholes formula actually means, why d1 and d2 exist, and how to price a call option in nine lines of Python.
Put-Call Parity, Explained
The no-arbitrage identity that links call price, put price, stock price, and strike — derived from first principles, no assumptions about direction or volatility.
Delta Hedging: What It Actually Means to Be Delta-Neutral
How market makers use delta to cancel out directional risk from an option position, worked through with real numbers and Python.
Theta Decay: Why Options Lose Value Every Day
What theta measures, why it accelerates as expiration nears, and why 'time decay' is a cost buyers pay and sellers collect — with the formula and Python.
Implied Volatility: What the Market Thinks Will Happen
Why implied volatility is Black-Scholes run backwards, how it's actually solved for with Newton-Raphson, and what the volatility smile tells you about the model's blind spots.
Vega, the Option Greek for Volatility Risk
Why vega is highest for at-the-money, longer-dated options, how it drives implied volatility solving, and how to compute it in Python.
Gamma Scalping: Trading the Curvature of Delta
What gamma measures, why it's highest at-the-money near expiration, and how gamma scalping turns constant delta-rehedging into a repeatable source of profit.
Binomial Option Pricing: The Discrete Alternative to Black-Scholes
How the binomial tree model prices options by stepping through discrete up/down moves, why it converges to Black-Scholes, and why it's the only method that handles American exercise cleanly.
CAPM and Beta: Why Some Risk Gets Paid and Some Doesn't
The Capital Asset Pricing Model explained from the diversification argument up — why beta is the only risk the market compensates you for, worked with real Python.
The Efficient Frontier in Python
How Markowitz mean-variance optimization builds the efficient frontier, why the covariance matrix is the hard part, and how to trace the frontier yourself with basic Python.
How to Backtest a Trading Strategy in Python Without Fooling Yourself
A working backtest framework, the metrics that actually matter (Sharpe, max drawdown), and the five biases that make backtests lie — with Python.
Monte Carlo Option Pricing, From Scratch
How Monte Carlo simulation prices options by simulating thousands of random stock paths under geometric Brownian motion, and why it's the tool of choice once Black-Scholes stops applying.