A bond's price is determined by the present value of its future cash flows, which include periodic coupon payments and the return of face value at maturity. The discount rate used is the yield to maturity (YTM), which represents the market's required rate of return. When a bond's coupon rate exceeds the market yield, the bond trades at a premium (above face value); when the coupon rate is below the market yield, it trades at a discount.

Interest rates and bond prices have an inverse relationship -- when interest rates rise, existing bond prices fall because newer bonds offer higher yields. Conversely, when rates decline, existing bonds with higher coupons become more valuable. This fundamental relationship is the cornerstone of fixed-income investing and drives much of the activity in bond markets worldwide.

A premium bond sells above its face value because its coupon rate is higher than the prevailing market yield. Investors are willing to pay more for the higher coupon income. Over time, a premium bond's price gradually decreases toward face value as it approaches maturity -- a process known as amortization of premium. Despite the higher purchase price, the total return includes both coupon income and the capital loss at maturity.

A discount bond sells below face value because its coupon rate is lower than the market yield. Investors pay less to compensate for the lower coupon income. As the bond approaches maturity, its price gradually increases toward face value -- known as accretion of discount. This capital appreciation combined with coupon payments provides the total return. Zero-coupon bonds are the most extreme discount bonds, purchased at a significant discount and paying no periodic interest.

While the bond pricing formula provides a theoretical fair value, actual market prices may differ due to factors like credit risk, liquidity, tax considerations, and market sentiment. Credit risk affects the yield spread over risk-free government bonds -- higher-risk issuers must offer higher yields, resulting in lower bond prices. Liquidity is also important, as less frequently traded bonds may carry a liquidity premium.

Call provisions can significantly impact bond pricing. Callable bonds give the issuer the right to redeem the bond before maturity, typically when interest rates decline. This limits the upside for investors in falling rate environments and often results in lower prices compared to non-callable bonds. Always consider the yield-to-call in addition to yield-to-maturity when evaluating callable bonds.