The term structure of an interest rate basis curve is defined as the relationship between the basis zero rate and it’s maturity. Basis curves are used as the forecast curves for pricing interest rate products. The increase in basis spreads has resulted in large impacts on non-standard instruments.

Overnight index swaps (OIS) curves became the market standard for discounting collateralized cashflows. The reason often given for using the OIS rate as the discount rate is that it is derived from the fed funds rate and the fed funds rate is the interest rate usually paid on collateral. As such the fed funds rate and OIS rate are the relevant funding rates for collateralized transactions.

An implied volatility is the volatility implied by the market price of an option based on the Black-Scholes option pricing model. A volatility surface is derived from quoted volatilities that provides a way to interpolate an implied volatility at any strike and maturity.

An interest rate swaption volatility surface is a four-dimensional plot of the implied volatility of a swaption as a function of strike and expiry and tenor.