Bond valuation

Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.

In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Various related yield-measures are then calculated for the given price. Where the market price of bond is less than its par value, the bond is selling at a discount. Conversely, if the market price of bond is greater than its par value, the bond is selling at a premium. For this and other relationships between price and yield, see below.

If the bond includes embedded options, the valuation is more difficult and combines option pricing with discounting. Depending on the type of option, the option price as calculated is either added to or subtracted from the price of the "straight" portion. See further under Bond option. This total is then the value of the bond.

Bond valuation

The fair price of a "straight bond" (a bond with no embedded options; see ) is usually determined by discounting its expected cash flows at the appropriate discount rate. Although this ''Present value'' relationship reflects the theoretical approach to determining the value of a bond, in practice its price is (usually) determined with reference to other, more liquid instruments. The two main approaches here, ''Relative pricing'' and ''Arbitrage-free pricing,'' are discussed next. Finally, where it is important to recognise that future interest rates are uncertain and that the discount rate is not adequately represented by a single fixed number—for example when an option is written on the bond in question—stochastic calculus may be employed.Fabozzi, 1998

Present value approach

The basic method for calculating a bond's theoretical fair value, or intrinsic worth, uses the present value (PV) formula shown below, using a single market interest rate to discount cash flows in all periods. A more complex approach would use different interest rates for cash flows in different periods. The formula shown below assumes that a coupon payment has just been made (see below for adjustments on other dates).

:$\begin TFV &= \begin \left(\frac+\frac+ ... +\frac\right) + \frac \end\\ &= \begin \left(\sum_^N\frac\right) + \frac \end\\ &= \begin C\left(\frac\right)+M(1+i)^ \end \end$
:where:
::$F =$ par value
::$i_F =$ contractual interest rate
::$C = F * i_F =$ coupon payment (periodic interest payment)
::$N =$ number of payments
::$i =$ market interest rate, or required yield, or observed / appropriate yield to maturity (see below)
::$M =$ value at maturity, usually equals par value
::$TFV =$ theoretical fair value

Relative price approach

Under this approach—an extension, or application, of the above—the bond will be priced relative to a benchmark, usually a government security; see Relative valuation. Here, the yield to maturity on the bond is determined based on the bond's Credit rating relative to a government security with similar maturity or duration; see Credit spread (bond)

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