 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/29k/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Let

τ = T - t

. Conditional on

F_{t}

S_{T} = S_{t} exp (σ (W_{T}^{Q} - W_{t}^{Q}) + (r - \frac{1}{2} σ^{2}) τ) .

V_{t} = S_{t}^{γ} exp [((γ - 1) r + \frac{1}{2} γ (γ - 1) σ^{2}) (T - t)] .

In particular,

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

Δ_{t} = \frac{\partial V}{\partial S} (t, S_{t}) = γ S_{t}^{γ - 1} exp [((γ - 1) r + \frac{1}{2} γ (γ - 1) σ^{2}) (T - t)]

units of the risky asset.

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