 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/29k/c/solution

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

Risk-neutral valuation gives

V_{0} = e^{- r T} E_{Q} [S_{T}^{p}] .

Since

W_{T}^{Q} \sim N (0, T)

E_{Q} [S_{T}^{p}] = S_{0}^{p} exp [p (r - \frac{1}{2} σ^{2}) T + \frac{1}{2} p^{2} σ^{2} T] .

V_{0} = S_{0}^{p} exp (((p - 1) r + \frac{1}{2} p (p - 1) σ^{2}) T) .

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