 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-4/29k/c/solution

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

Let

N = T - t

and use the discounted multipliers

u, d

. Under

Q

K

of up moves in the remaining

N

Binomial (N, q)

. Since

S_{T}^{1} = S_{t}^{1} u^{K} d^{N - K},

V_{t} = k = 0 \sum T - t (k T - t) q^{k} (1 - q)^{T - t - k} h (S_{t}^{1} u^{k} d^{T - t - k}) .

For an undiscounted stock, replace

u, d

U, D

and discount the resulting payoff by the appropriate power of

R

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