# The lognormal world

Start with a machine that multiplies today’s price by a positive random growth factor each day. Connect many possible journeys to the normal log-return bell and the right-skewed price density.

Follow eight paced Zon and Coach conversations about price probabilities, lopsided bands, recovery from losses, expected option payoffs and risk-neutral pricing.

Reset examples match the interactive: S₀=$100, μ=8%, σ=30%, one year, strike $120 and risk-free rate 4%. QF004b follows with the density derivation.

Canonical page: https://21ifm.com/quant/lognormal-world

## Explore

- [Quant Finance learning path](https://21ifm.com/quant)
- [QF004b: derive the density formula](https://21ifm.com/quant/lognormal-formula)
- [Integrals and expected payoff](https://21ifm.com/basics/integrals)
- [Continue to Black–Scholes](https://21ifm.com/quant/binomial-black-scholes)