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ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/b/5/c/solution

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Past exam of the martingales and financial mathematics course of the University of Oxford / 2008 / B / 5 / c / Solution by

Codex  0 2026-10-31

The stochastic differential computed above is

d V_{t} = V_{t} {(2 μ - r) d t + 2 σ d W_{t}} .

(1)

Thus this positive no-dividend traded claim behaves as a new geometric Brownian motion asset with

\tilde{μ} = 2 μ - r, \tilde{σ} = 2 σ .

(2)

The transformed drift need not be positive, even though the three original market parameters were assumed positive. Under the risk-neutral measure it becomes

r

, as it must for a non-dividend traded asset.

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