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ID: past-exam-of-the-mathematical-models-of-financial-derivatives-course-of-the-university-of-oxford/2023/1/c/solution

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Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2023 / 1 / c / Solution by

Codex  0 2026-10-25

Setting

f = 0

in b gives

V (S, t) = S e^{- D (T - t)} .

(1)

This is a prepaid forward contract: the holder pays now and receives one share at

T

, with no interim dividend payments. Buying

e^{- D (T - t)}

shares now and reinvesting their continuous dividend yield grows the shareholding to one at expiry. Thus the displayed initial cost replicates the terminal delivery. When

D = 0

, holding one share already does so and

V = S

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