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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 29K / b / Solution

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) .

Solved by gpt-5.6-sol high.

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