Bond ValuationThe determination of a bond's fair price is defined as bond valuation [1].

Face ValueThe printed amount on the bond is called as face value [2].

Coupon RateCoupon rate is the rate at which the bond pays interest on its face value at regular time intervals until the redemption date [2].

Let

= Face Value

= Coupon Rate

= Yield to Maturity

= Number of Years

= Payment Frequency

= Cash Flow

= Coupon Payment

= Bond Value

= Maculay Duration

= Modified Duration

= Convexity

Coupon Payment can be calculated as the following:

We can calculate Bond Value by using the following formula:

Then, Maculay duration can be calculated as follows:

We can also calculate Modified Duration:

Then, convexity can be calculated as the following:

where

, if

, otherwise.

and is the present value function.

**Example 1**

*Input*

Face Value = 1000

Coupon Rate = 8%

Yield to Maturity = 8%

Years = 6

Frequency = Semiannually

*Output*

Bond Value = 1000

Maculay Duration = 4.88

Modified Duration = 4.69

Convexity = 27.227

**Example 2**

*Input*

Face Value = 1000

Coupon Rate = 14

Yield to Maturity = 16

Years = 7

Frequency = Quarterly

*Output*

Bond Value = 916.685

Maculay Duration = 4.454

Modified Duration = 4.282

Convexity = 25.057

1. Bond valuation (n.d.). Retrieved August 18, 2016, from https://en.wikipedia.org/wiki/ Bond_valuation

2. Bonds and Bond Pricing. (n.d.). Retrieved from http://www.mysmu.edu/faculty/ yktse/FMA/S_FMA_6.pdf