Use a two-period binomial model to value an interest rate option and explain the result
The idea
Interest rate options use an arbitrage-free tree of one-period rates, with probabilities of 0.5 on each branch. The underlying is a rate, so a call (like a caplet, but paid when the rate is set) pays notional × max(0, rate − strike) and a put (like a floorlet) pays notional × max(0, strike − rate), adjusted for the accrual period. Work out the payoffs at the end nodes, then roll back: each node's value is the average of the two values that follow it, discounted at the rate at that node rather than at one flat rate. The trap is discounting everything at today's rate, or reporting a later node's value as if it were today's price.
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