Option pricing: a discrete perspective
July 22, 2025
In these notes, we cover the basics of option pricing, starting with how derivatives pay off and the put-call parity relationship. We introduce risk-neutral probabilities, which are the key tool for pricing derivatives; they let market makers hedge their positions instead of gambling on price movements. We build up the binomial pricing model step by step, showing how no-arbitrage arguments and hedging naturally give us option prices. Finally, we extend this to multi-step trees and show how they converge to the Black-Scholes formula, connecting discrete hedging to continuous-time pricing.