Bond Pricing Explained: How Bond Prices Are Determined
Why Bond Prices Change
Imagine you hold a bond paying a 3% coupon. If new bonds start paying 5%, nobody will pay full price for your 3% bond — so its price drops until the effective yield matches current rates. The reverse happens when rates fall: your 3% bond becomes more valuable when new bonds only pay 2%.
This is why bond prices are quoted as a percentage of face value. A price of 98 means the bond trades at 98% of par ($980 for a $1,000 bond). A price of 103 means it trades at a premium ($1,030). At exactly 100, the bond trades at par.
The Bond Pricing Formula
Where: C = coupon payment per period, r = market yield per period, n = number of periods to maturity, FV = face value. The first part calculates the present value of all coupon payments (an annuity). The second part calculates the present value of the face value repayment.
Pricing Example
A 5-year bond with a 4% annual coupon, $1,000 face value, and the market yield is 5%:
| Component | Calculation | Value |
|---|---|---|
| PV of Coupons | $40 × [1 − (1.05)⁻⁵] / 0.05 | $173.17 |
| PV of Face Value | $1,000 / (1.05)⁵ | $783.53 |
| Bond Price | $173.17 + $783.53 | $956.70 |
The bond trades at a discount ($956.70 < $1,000) because the coupon rate (4%) is below the market yield (5%). Investors need a lower price to achieve the higher market-required return.
Premium, Discount, and Par
| Scenario | Coupon vs. Market Yield | Price |
|---|---|---|
| Premium | Coupon rate > market yield | Above $1,000 |
| Par | Coupon rate = market yield | Exactly $1,000 |
| Discount | Coupon rate < market yield | Below $1,000 |
As a bond approaches maturity, its price converges toward par value regardless of where it started. This “pull to par” effect means premium bonds gradually decline in price and discount bonds gradually increase — assuming no default.
Factors That Affect Bond Prices
Interest rate changes are the primary driver. The Federal Reserve’s monetary policy decisions move the entire yield curve and directly impact bond prices. Longer-maturity bonds are more sensitive to rate changes — a concept measured by duration.
Credit quality changes also move prices. If a company’s credit rating gets downgraded, its bond prices fall because investors demand a higher yield to compensate for increased default risk. The spread between corporate bond yields and Treasury yields widens during economic stress.
Time to maturity matters because longer bonds have more future cash flows exposed to discounting. A 30-year bond will experience much larger price swings than a 2-year note for the same rate change. Learn more about this sensitivity in our Duration and Convexity guide.
Supply and demand also play a role. When investors flee to safety during market turmoil, demand for Treasuries spikes and prices rise (yields fall). This “flight to quality” is why bonds often rally when stocks crash.
Clean Price vs. Dirty Price
Bond prices are quoted as the clean price — without accrued interest. But when you actually buy a bond, you pay the dirty price (also called the invoice price), which includes accrued interest since the last coupon date. The seller earned that interest during the period they held the bond, so you compensate them for it.
Key Takeaways
- Bond prices are the present value of future coupon payments plus the face value at maturity.
- Prices move inversely to interest rates — this is the foundational rule of bond investing.
- Bonds trade at a premium (above par), at par, or at a discount (below par) depending on how coupon rates compare to market yields.
- Longer-maturity bonds experience larger price swings for the same rate change — measured by duration.
- You pay the dirty price (clean price + accrued interest) when buying a bond between coupon dates.
Frequently Asked Questions
Why do bond prices go down when interest rates go up?
Because existing bonds must compete with newly issued bonds. When new bonds offer higher coupons, older bonds with lower coupons become less attractive. Their prices drop until their effective yield matches the new market rate.
What does it mean when a bond trades at a discount?
A bond trading at a discount (below par value) has a coupon rate below the current market yield. You buy it for less than $1,000 but receive the full $1,000 at maturity, so the discount effectively boosts your return to match market rates.
How do I calculate a bond’s current yield?
Current yield = Annual coupon payment ÷ Current market price. A bond with a $40 annual coupon trading at $950 has a current yield of 4.21%. Note this differs from yield to maturity, which also accounts for the price gain or loss at maturity.
What is accrued interest on a bond?
Accrued interest is the interest a bond has earned since its last coupon payment date. When you buy a bond between coupon dates, you pay the seller this accrued interest on top of the quoted price. You’ll recoup it when you receive the next full coupon payment.
Do bond prices always return to par at maturity?
Yes, assuming the issuer doesn’t default. As the maturity date approaches, the bond’s price gradually converges to par value. This “pull to par” happens because the remaining cash flows shrink, reducing the impact of any yield difference.