Exercise 9.8 Suppose that claim holders will receive a fraction of contingent claim X, rather than the market value, at default epoch. Denoting the fraction by δ, confirm that the time-t price of the contingent claim is given by

This recovery formulation is called the recovery of face value (RFV) and originally considered by Madan and Unal (1998). Now, assuming that all the parameters except the recovery formulation are the same, prove that

where va(t, T) denotes the time-t price of the defaultable discount bond under recovery formulation

a, a = RMV, RT, or RFV.

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X C(t) = B(t)EQ 6 B(T) 1{+>T} + -1{T} B(T)