 Solution

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

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

The terminal payoffs satisfy the pointwise identity

(K - S_{N})^{+} - (S_{N} - K)^{+} = K - S_{N} .

Pricing both sides by discounted risk-neutral expectation gives

EP (N, K) - EC (N, K) = (1 + r)^{- N} K - S_{0},

because the discounted stock is a martingale. Thus put-call parity is

EP (N, K) = (1 + r)^{- N} K - S_{0} + EC (N, K) .

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