 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-1/28j/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

For positive

S_{0}, K, T, σ

d_{1} = \frac{lo g ( S _{0} / K ) + ( r + σ ^{2} /2 ) T}{σ T}, d_{2} = d_{1} - σ T .

To hedge the sold European call option, buy

Φ (d_{1})

shares and borrow

K e^{- r T} Φ (d_{2})

in cash. This long replicating strategy has initial value

S_{0} Φ (d_{1}) - K e^{- r T} Φ (d_{2})

, financed by the option premium. The share holding must subsequently be rebalanced according to the option's option delta in a self-financing strategy.

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