Concept
One of the many factors that you should consider before investing in a bond is its market price. But how to determine the price of a bond? In this article, I discuss the popular methods of bond valuation or bond pricing.
Buying a bond, you are entitled to periodic interest payment and also to the principal amount at maturity. The cash flows on a bond are fixed by nature. But the market price of the bond changes depending on the prevailing interest rate. If the market interest rate is higher, the yields from a bond have fewer values and so the price of the bond falls and vice versa.
The price of a bond is the summation of present values of future interest payments plus to the present value of the par value at maturity. This present value is obtained by discounting future values by an appropriate discount rate, called yield to maturity (YTM). The minimum yield to maturity for a risk-free bond (government bonds) should equal the interest rate.
Calculation
When it comes to bond pricing method, usually there are a couple of options. I have discussed here four methods, starting from a very straight forward approach gradually progressing to relatively complex ones.
1. Present Value Method
For a straight bond without any embedded options, the formula for determining its price isWhere
P = the current price of the bond
C = size of the cash flow
r = discount rate (market interest rate or required yield)
M = value of the bond at maturity or face value
N= number of periods
2. Relative Pricing Method
This bond pricing method is to be used to determine the value of a risky bond. The method is pretty similar one with the only difference that while computing the price, the bond is compared with a benchmark, usually a government bond.
The yield to maturity of this bond includes an extra allowance for the associated risk compared to a government bond of similar maturity. This allowance is called the credit spread. The better the reputation of the bond, the smaller the spread and vice versa. This spread value affects only the r in the above formula and the rest remains the same.
3. Rational Pricing Method
A rather modern approach to valuing bonds is to consider the bond as a basket of multiple zero-coupon bonds. Each zero-coupon bond matures as the cash flow is received. They are valued and discounted individually and at the end added together to give the final price of the bond. The rationale is to obtain an arbitrage-free pricing.
4. Stochastic Calculus Method
In all of the aforementioned methods, it is assumed that we know the future interest rate and consequently the YTM to discount the future cash flows and par value accurately. But this is far from reality.
Using calculus to determine bond prices is a rather realistic approach. In this method, a random variable is used to incorporate the uncertainty aspect into the calculation.
