Valuing a zero-coupon bond

A zero-coupon bond is a bond that does not pay any periodic interest except on maturity, where the principal or face value is repaid. Zero-coupon bonds are also called pure discount bonds.

A zero-coupon bond can be valued as follows:

Here, is the annually compounded yield or rate of the bond, and is the time remaining to the maturity of the bond.

Let's take a look at an example of a 5-year zero-coupon bond with a face value of $100. The yield is 5 percent, compounded annually. The price can be calculated as follows:

A simple Python zero-coupon bond calculator can be used to illustrate this example:

def zero_coupon_bond(par, y, t):
    """
    Price a zero coupon bond.
    
    Par - face value of the bond.
    y - annual yield or rate of the bond.
    t - time to maturity in years.
    """
    return par/(1+y)**t

Using the preceding example, we get the following result:

>>> print zero_coupon_bond(100, 0.05, 5)
78.3526166468

In the preceding example, we assumed...