A Unified Approach to Interest Rate Risk and Credit Risk of Cash and Derivative Instruments

Abstract

A bond priced different from par is really a par bond plus an instrument whose value equals that deviation from par. A pure interest rate derivative, such as a bond futures contract or an interest rate swap, reflects only the deviation component of the bond, as there is no “principal,” or par value. A bond with credit risk equals a credit riskless bond plus an instrument containing the compensation for credit risk. A credit default swap reflects only this second component. Approaching bonds this disaggregated way provides clear insight into why and to what degree bonds move away from par, and how these derivatives can hedge those movement from par. Furthermore, it explains why floating rate notes have some degree of interest rate sensitivity, despite their regular coupon adjustment to the market, and why an asset swap, which combines a corporate bond with an interest rate swap, is not a “synthetic corporate bond.” Keywords: bond price equation; par bond; risk-free rate; coupon; present value; duration; pure interest rate derivative; corporate bond; credit spread; annuity; credit risk discounting; interest rate swap; floating rate note; London Interbank Offered Rate (LIBOR); counterparty; asset swap; bankruptcy; default; credit default swap