Bond valuation is the process of estimating the fair value of a bond. In the present-value approach, the value equals the sum of expected cash flows discounted at appropriate rates.

In practice the discount rate is often inferred by reference to similar, more liquid instruments. Several related yield measures can then be computed for a given price (see Yield and price relationships). If the market price of a bond is below par value, it trades at a discount; if it is above par, it trades at a premium. Methods used on this page include relative pricing and arbitrage-free pricing.

If a bond has embedded options, valuation combines option pricing with discounting. Depending on the option type, the option value is added to or subtracted from the value of the option-free bond to obtain the total price. See embedded options.

The fair price of a “straight” bond (no embedded options - see bond features) is the present value of its expected cash flows discounted at appropriate rates. In practice, prices are often inferred relative to more liquid instruments. Two approaches are common: relative pricing and arbitrage-free pricing. When valuation must reflect uncertainty in future rates, for example when valuing a bond option, analysts use interest-rate models.

A basic calculation discounts each cash flow at a single market rate for all periods. A more realistic variant discounts each cash flow at its own rate along the curve. The formula below assumes a coupon has just been paid. See clean and dirty price for other dates. $${\displaystyle P\;=\;\sum _{n=1}^{N}{\frac {C}{(1+i)^{n}}}\;+\;{\frac {M}{(1+i)^{N}}}\;=\;C\,{\frac {1-(1+i)^{-N}}{i}}\;+\;M\,(1+i)^{-N}.}$$ where:

Under this approach the bond is priced relative to a benchmark, usually a government bond yield curve. Set the bond’s yield to maturity as the benchmark yield plus a credit spread appropriate to its credit rating and maturity or duration. Use this required return in the present-value formula above by replacing ${\displaystyle i}$ with the bond’s YTM.

Under this approach each promised cash flow is valued at its own discount rate. View the bond as a package of cash flows and discount each one at the rate implied by a matching zero-coupon of the same maturity and credit quality.

Let ${\displaystyle CF_{n}}$ be the cash flow at time ${\displaystyle t_{n}}$ and ${\displaystyle Z(0,t_{n})}$ the discount factor for that date. Then $${\displaystyle P\;=\;\sum _{n=1}^{N}CF_{n}\,Z(0,t_{n}).}$$