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Forward contract on a defaultable coupon bearing bond

Notations : $P(t,T)$ : the $t$-price of a coupon bearing bond paying coupons $C_i$ at $T_i$ maturing at $T$ $B(t,T)$ : the $t$-price of a non defaultable zero coupon bond paying 1 at $T$ $P_r(t,T)$ : ...
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