The Rebate Value Process with Some Applications

Abstract

In the pricing of credit derivatives default is modelled as a stopping time and prices are typically determined by separation of cash-flows before and at default. In a general risk-neutral valuation setting, this technique suggests the decomposition of an asset which holds even if the asset is not credit-sensitive. The rebate value process is introduced and related to the price of an asset before and after default. The financial interpretation of this process is different depending on the type of asset decomposed. An interpretation of recovery is illustrated by pricing several standard credit-sensitive assets including a risky coupon bond and a credit default swap (CDS). An interpretation of insurance is illustrated by pricing the complements of the credit ``building blocks'' with respect to the stopping time. Several applications of these complements are presented including a risky interest rate swap and a full-recovery CDS.