- Sources of Return from Investing in a Bond
- How to Calculate Current Yield
- How to Calculate Yield to Maturity
- Bond Equivalent Yield Convention
- Yield to Maturity (YTM) Approximation Formula
- YTM and Reinvestment Risk
- Factors Affecting Reinvestment Risk
- Calculate Bond-Equivalent Yield of Annual-Pay Bonds
- How to Calculate Yield to Call of a Bond
- Cash Flow Yield
- Bootstrapping Spot Rate Curve (Zero Curve)
- How to Price a Bond Using Spot Rates (Zero Curve)
- Nominal Spread
- Z-Spread: Definition and Calculation
- Option-adjusted Spreads (OAS)
- What are Forward Rates?
- How to Calculate Forward Rates from Spot Rates?
- How to Value a Bond Using Forward Rates

# How to Price a Bond Using Spot Rates (Zero Curve)

The simplest way to calculate the value of a bond is to take the cash flows of the bond till its maturity and then discount them by a single discount rate. The method is quick but not very accurate because the yield curve is not flat and the interest rates are different for different maturities. A better way to price the bonds is to discount each cash flow with the spot rate (zero coupon rate) for its respective maturity.

**Example 1**

Let’s take an example. Suppose we want to calculate the value of a $1000 par, 5% coupon, 5 year maturity bond. We also have the following spot rates for the next 5 years:

Assuming this is an annual pay bond, the bond will have the following cash flows.

Year 1: $50

Year 2: $50

Year 3: $50

Year 4: $50

Year 5: $1000 + $50

The value of the bond can be calculated by discounting these cash flows by their respective spot rate.

Bond Value = 50/(1.04)^1+50/(1.0430)^2+50/(1.0451)^3+50/(1.047)^4+1050/(1.048)^5

Bond Value = $1010.033

**Example 2**

Let’s take another example. Suppose we have a bond that matures in 2 years, that has a coupon rate of 6%, and pays coupon semi-annually. The spot rates are 3.9% for 6 months, 4% for 1 year, 4.15% for 1.5 years, and 4.3% for 2 years.

The cash flows from this bond are $30, $30, $30, and $1030.

The value of the bond will be calculated as follows:

Bond value = $30/(1+3.9%/2)^1+$30/(1+4%/2)^2+$30/(1+4.15%/2)^3+$1030/(1+4.3%/2)^4

Bond value = $1032.45

You can use the above formula to value any bond with any maturity. All you need is the spot rate for the respective maturity. Since **spot rates are bootstrapped from yield curve**, we may have to interpolate yields for certain maturities for which Treasury securities are not available.

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