Interest Rate Swap Valuation and Applications › Summary

This chapter developed the analytical tools for valuing and applying interest rate swaps:

• Valuation Approaches: Swaps can be valued as portfolios of bonds (long fixed, short floating) or portfolios of forward rate agreements. Under the stated assumptions, both methods yield identical values. The two approaches offer complementary views of swap economics.
• The Swap Curve: Market par swap quotes can be calibrated into discount factors under a stated schedule and interpolation convention; the resulting discount and projection curves are inputs to an interest-rate valuation model, not a complete model for every derivative. Historically, unsecured IBOR swap curves reflected bank funding premia; RFR OIS curves instead reference near-risk-free overnight rates and do not generally measure unsecured term bank funding.
• Par Swap Rate: For matching payment schedules in the single-curve model, the par swap rate is an accrual- and discount-factor-weighted average of simple forward rates that gives a swap zero initial value. An interpretation as average expected short-term rates requires additional model and risk-premium assumptions.
• Mark-to-Market Valuation: As rates change, existing swap positions can gain, lose or remain unchanged. The displayed positive-DV01 receive-fixed examples gain locally from parallel rate declines; reversing the position reverses that sensitivity. Determine the sign from the remaining cash flows and fixing state, not the receive-fixed or pay-fixed label alone.
• Risk Measures: Signed DV01 is local first-order value sensitivity per basis point under a specified curve shock. Reprice finite moves separately. Notional-normalized swap sensitivity depends on the fixed-bond cash-flow weights, curve and floating-reset exposure. Calculate it from signed DV01 with a stated shock and normalization; there is no universal half-maturity rule.
• Practical Applications: Swaps enable hedging (converting floating exposure to fixed), synthetic asset creation (combining floating assets with swaps to create synthetic fixed instruments), and asset-liability management (adjusting duration gaps).

Understanding swap valuation opens the door to credit derivatives and structured products. In the next chapter, we'll examine credit default swaps, which apply similar contractual structures to credit risk rather than interest rate risk.