Spot Curve

Also called the Discount Curve or Zero Rate Curve

Also known as Term Structure of Interest Rates, Risk Free Zero Coupon Curve, Nominal Zero Coupon Yield Curve, zero rates, spot rate yield curve, implied zero coupon curve, zero spot curve, spot interest rates, zero coupon spot rate, Interpolated Yield Curve, I-Curve

A spot rate is the discount rate used to calculate todays value of a future cash flow.
Converts a future cash flow to todays value.
This is used to convert a future cash flow to its present value.

this interest rate is called a spot rate or discount factor

Theoretical Curve

This is an "implied" or "theoretical curve
This the relationship between the yield to maturity on a zero coupon bond and the bonds maturity date.
This is a sequence of such risk-free rates with varying maturities.
Only zero-coupon bonds have no reinvestment risk associated with them.
It is the reinvestment risk (or assumption) that makes this curve a better choice than the Yield to Maturity curve.
Zero-coupon yields are the key determinant of value in the capital markets and they are calculated and quoted for every major currency.
Zero coupon yields can be used to value any cash flow that occurs at a future date.
These can be used as a benchmark for pricing bonds.

Constructing using Government Bonds/Securities

US Treasury STRIPS
The yields on coupon strips are by definition zero coupon rates.
on the run
coupon paying treasury bonds
Could use UK government bonds
If US Treasuries are used, the curve is often called the Treasury Spot Curve

Constructing using LIBOR/Swaps

Important

It is called the zero volatility spread because we have not allowed for volatility. We assume the rates are deterministic.
The yield on a zero-coupon intrument is called the spot rate.
The zero-coupon yield curve is not an accurate indicator of average market yields because most bonds are not zero-coupon.
This is the best curve to use when determining the relative value.