Valuation of Interest Rate Derivatives › Summary

Interest rate derivatives extend the option framework to the rates market, and gives useful tools for hedging and speculation on interest rate movements. The key concepts from this chapter include:

Caps and Floors are portfolios of options on interest rates. A cap protects against rising rates by paying you when the reference rate exceeds the strike. A floor protects against falling rates. Black's model provides the standard pricing framework, treating each caplet or floorlet as an option on a forward rate with lognormal dynamics.

Swaptions are options to enter interest rate swaps. Payer swaptions benefit when rates rise above the strike, while receiver swaptions benefit when rates fall. Black's model again provides the standard approach, now applied to forward swap rates. Bermudan swaptions, with multiple exercise dates, require more sophisticated lattice or simulation methods.

Risk measures for interest rate derivatives extend the Greeks framework. PV01/DV01 measures sensitivity to rate levels, while vega captures volatility exposure. Understanding these sensitivities is essential for hedging and risk management.

Practical applications span corporate hedging, bank risk management, and structured product creation. The option-adjusted spread framework helps evaluate securities with embedded optionality, such as mortgage-backed securities.

These models have limitations regarding distributional assumptions, calibration stability, and correlation. You understand both the theoretical framework and its practical boundaries.