 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/b/8/a/solution

The risk-neutral one-step mean multiplier must equal the bank growth factor:

q u + (1 - q) d = e^{r} = 1.05.

q = \frac{1.05 - 0.9}{1.1 - 0.9} = \frac{3}{4}, 1 - q = \frac{1}{4} .

It lies strictly between zero and one, consistent with the no-arbitrage inequality

d < e^{r} < u

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