Explain the binomial model for valuing options and what each of its terms means
The idea
In the binomial model the price moves each period to S × u or S × d. Value comes from a riskless hedge of h units of the underlying per option, where the hedge ratio is h = (c+ − c−) ÷ (S+ − S−). The hedged position must earn the risk-free rate, which pins down the option's value. Equivalently, use the risk-neutral probability π = (1 + r − d) ÷ (u − d) and discount the probability-weighted payoffs at r. No arbitrage requires d < 1 + r < u. The trap is treating π as a forecast of the real chance of an up move, when it is only a pricing weight.
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