# Spot Curve

Also known as **Zero Coupon Yield Curve**, **Term Structure of Interest Rates**, interest-rate swap curve, zero curve, implied zero coupon curve, zero spot curve, risk-free zero curve, zero coupon spot rate, zero coupon rates

The is the relationship between the yield to maturity on a zero coupon bond and the bonds maturity date.

These can be used as a benchmark for pricing bonds.

### Theoretical Curve

This is an "implied" or "theoretical curve

This is a sequence of such risk-free rates with varying maturities.

We cannot observe such a curve in the market

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.

### Yield to Maturity of Zero Coupon Bonds = Spot Rate

A spot rate is the discount rate that converts a future cash flow to its present value

The yield to maturity of a zero-coupon bond is the discount rate that converts the par value to its present value.

### Using Government Issued Securities

US Treasury STRIPS

The yields on coupon strips are by definition zero coupon rates.

on the run

coupon paying reasury bonds

Could use UK government bonds

### Using the Interest Rate Swaps Markets

Interbank Deposits

Interest Rate Forwards

Short term interest rate futures

Interest Rate 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.

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