Defaults payout

For each moment in the life of the default swap we can sum up all of the instantaneous chances of actually receiving a default payout of 1 - R by integrating the above equation from time 0 to the maturity date, T. However, we need to make one adjustment, and that is to weight each chance of default by its present value. It is only appropriate that receiving a payout of 1 - R is worth more if that payout occurs tomorrow rather than next year, so after weighting each potential payout by its appropriate discount factor the value of the default protection becomes... 

Default payout period value 3 yr/payout period ... 

For credit derivative contracts in which the payout is on credit events other than default, the modeling of the credit evolutionary path is critical. If, however, a credit derivative contract does not payout on intermediate stages between the current state and default then the important factor is the probability of default from the current state. 

In the event of a default, there will be no payment of accrued interest by the issuer since generally coupons are not recoverable, so we can ignore that aspect of the valnation. The only component left to the bond is its value upon a default or its recovery value. If a default occurs, the bondholder will lose all future cash flows of the instrument (i.e., they are at risk), but will be left with a nonperforming asset worth R. The same technique is used here as in the default swap—except this time the payout is R rather than 1 - R upon default. Conveniently, this formula is identical to equation (22.11), except that the term (1 - R) is replaced by R. 

Credit-derivative pricing is similar to the pricing of other off-balance-sheet products, such as equity, currency, and bond derivatives. The main difference is that the latter can be priced and hedged with reference to the underlying asset, and credit derivatives cannot. The pricing model for credit products incorporates statistical data concerning the likelihood of default, the probability of payout, and market level of risk tolerance. 

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