 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-4/29k/c/solution

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

5

pays

2, 0, 0

at terminal stock prices

7, 5, 3

. Its lower-node value is zero, while its upper-node value is

V_{u} = R^{- 1} (\frac{7}{8} \cdot 2) = \frac{14}{9} .

V_{0} = R^{- 1} \frac{13}{16} \frac{14}{9} = \frac{91}{81} .

By the fundamental theorem of asset pricing, this discounted expectation under the unique risk-neutral probabilities is the unique no-arbitrage price.

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