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Risk-neutral probability in a binomial market

If the stock factors are

1 + a

and

1 + b

and the risk-free factor is

1 + r

, the discounted stock is a martingale under the probability

q = \frac{r - a}{b - a}

of an up move. The probability of a down move is

(b - r) / (b - a)

.

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