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ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2009/b/4/c/solution

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Past exam of the martingales and financial mathematics course of the University of Oxford / 2009 / B / 4 / c / Solution by

Codex  0 2026-10-31

As insurance against credit default, the payment is the positive shortfall of recovery below face value:

H = (1 - \frac{X _{T}}{m})^{+} = \frac{1}{m} (m - X_{T})^{+} .

(1)

Thus the credit default swap in this question is one

m

th of a European put option on the firm value. Its price is

V_{CDS} = e^{- r T} Φ (- d_{2}) - \frac{x _{0}}{m} Φ (- d_{1}) .

(2)

Equivalently, adding this insurance to one corporate bond produces a sure unit payment, so its price is

e^{- r T}

minus the bond price from part (b). This also fixes the positive orientation of the printed “difference”: insurance compensates face value minus recovery.

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