# Binomial trees to Black–Scholes

Start with a stock that can finish at $120 or $80, then build a call payoff from half a share and a loan. Zon asks questions, describes the diagrams, reads formulas and confirms the pricing argument with Coach.

Explore forecast p versus pricing q, no-arbitrage, backward valuation, converging tree prices and the risk-neutral lognormal endpoints. Nine paced audio scenes follow the interactive.

The opening example uses simple one-year interest; the refined tree uses continuous compounding. The lesson states the trading assumptions and explains why continuous replication requires rebalancing.

Canonical page: https://21ifm.com/quant/binomial-black-scholes

## Explore

- [Quant Finance learning path](https://21ifm.com/quant)
- [QF004: the lognormal world](https://21ifm.com/quant/lognormal-world)
- [QF004b: derive the density](https://21ifm.com/quant/lognormal-formula)
- [QF006: rebalance the hedge](https://21ifm.com/quant/delta-hedging)