 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-4/29k/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Under a risk-neutral measure, the discounted stock must be a martingale. If

q

is the probability of the factor

1 + b

, this condition is

q (1 + b) + (1 - q) (1 + a) = 1 + r,

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

a < r < b

ensures

0 < q < 1

, making this equivalent to the original probability measure. Since the

N

returns are independent under

Q

Q (S_{N} = S_{0} (1 + b)^{i} (1 + a)^{N - i}) = (i N) q^{i} (1 - q)^{N - i} .

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