Risky Swaps

In [10] we presented a reduced form of risky bond pricing. At default date, a bond seller fails to continue fulfilling his obligation and the price of the bond sharply drops. For nodefault scenarios, if the face value of the defaulted bond is $1 then the bond price just after the default is its’ recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with the general debt problems is presenting the price, knowing the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price inversely depends on interest rate. In case of a default, the credit risk on a debt investment is related to the loss. There is a possibility for a risky bond buyer to reduce his credit risk. This can be achieved through buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which ever one comes first. If default comes before maturity, the protection buyer will receive the difference between the initial face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer; the opposite party is the CDS seller. Note, that in contrast to corporate bond, CDS contract does not assume that the buyer of the CDS is the holder of underlying bond. Also note that underlying to the swap can be any asset. It is called a reference asset or a reference entity. Thus, CDS is a credit instrument that separates credit risk from corresponding underlying entity. The formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default in case it occurs before the maturity. If default does occur, protection buyer delivers cash or a default asset in exchange with the face value of the defaulted debt. These are known as cash or physical settlements