 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-3/29k/c/solution

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

Condition on the first risk-neutral move. After a factor

1 + a

, homogeneity of the call payoff gives

((1 + a) S_{N} - K)^{+} = (1 + a) (S_{N} - \frac{K}{1 + a})^{+},

and the analogous identity holds for

1 + b

EC (N + 1, K) = u EC (N, \frac{K}{1 + a}) + v EC (N, \frac{K}{1 + b}),

with

u = \frac{( 1 + a ) ( b - r )}{( 1 + r ) ( b - a )}, v = \frac{( 1 + b ) ( r - a )}{( 1 + r ) ( b - a )} .

a < r < b

and

a > - 1

make both coefficients positive.

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