A Price With No Opinion in It - no-arbitrage, replication and the binomial tree

The valley’s water market, where the OPTION box says “the right, not the duty, to buy at a fixed price; you pay a premium for it”. This lesson works out what that premium has to be, without asking anyone what they think will happen.

Before you start. You need one idea from The Right, Not the Duty - options, calls, puts and the payoff: a call option is a paid right to buy something later at a price fixed today (the strike), so at the end it is worth the final price minus the strike if that is positive, and nothing otherwise. You also need, from Why a Coin Today Beats a Coin Next Year - present value and discounting, that money due later is worth a little less today; this lesson sets the interest rate to zero for most of the way so that part stays out of the arithmetic.