Introduction

Why Options Pricing?

Options are financial contracts that give the holder the right — but not the obligation — to buy or sell an asset at a fixed price before a given date. Pricing them correctly is one of the central problems of quantitative finance. The Black-Scholes formula, published in 1973, earned its inventors the Nobel Prize in Economics and launched the modern derivatives industry.

This course implements options pricing from first principles in pure Python. No scipy, no numpy — just the mathematics as code.

You will implement:

  • Basics — Call and put payoffs, put-call parity, intrinsic and time value
  • Black-Scholes — The closed-form formula using the normal CDF, plus implied volatility via bisection
  • Greeks — Delta, gamma, theta, vega, and rho — the sensitivities that drive hedging
  • Numerical Methods — Binomial trees (1-step and N-step), American options, Monte Carlo, Asian options, and barrier options
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