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

As insurance against credit default, the payment is the positive shortfall of recovery below face value:Thus the credit default swap in this question is one $m$th of a European put option on the firm value. Its price isEquivalently, adding this insurance to one corporate bond produces a sure unit payment, so its price is $e^{-rT}$ minus the bond price from part (b). This also fixes the positive orientation of the printed “difference”: insurance compensates face value minus recovery.