In the previous post, we saw an introduction about bonds, in this post we will see the formula for the price of a bond, before that we will introduce what is called the yield of a bond.

The Yield to Maturity (YTM) of a bond is the internal rate of return of a bond at it's market price, the price of a bond and it's yield are inversely proportional, if the price goes down, the yield goes up and vice-versa. A par-bond is one where the yield is equal to the interest rate (coupon rate).

Given the above definition, the price of a bond (P) is given by,

where

P = Price of the bond

F = Face value of the bond

C = Coupon payment per year

m = Number of periods in an year the coupon is paid (Typically m = 2 or coupons are paid every 6 months)

n = Number of coupon periods left (with m coupon periods per year)

λ = Yield to maturity

Lets look at an example from Investment Science by Luenberger to calculate the price of a bond (Problem 3.9).

Problem 3.9

An 8% bond with 18 years to maturity has a yield of 9%. What is the price of this bond.

In this problem, it is implied that the face value of the bond F = $100 (unless specified otherwise).

m = 2 (Unless explicitly specified, coupons are paid every 6 months in an year)

λ = 9%,λ/2 = 4.5%

Given the above definition, the price of a bond (P) is given by,

where

P = Price of the bond

F = Face value of the bond

C = Coupon payment per year

m = Number of periods in an year the coupon is paid (Typically m = 2 or coupons are paid every 6 months)

n = Number of coupon periods left (with m coupon periods per year)

λ = Yield to maturity

Lets look at an example from

Problem 3.9

An 8% bond with 18 years to maturity has a yield of 9%. What is the price of this bond.

In this problem, it is implied that the face value of the bond F = $100 (unless specified otherwise).

m = 2 (Unless explicitly specified, coupons are paid every 6 months in an year)

λ = 9%,

## 1 comment:

Thanks a lot for your post on Investment science. It helps !! I have taken a course on it at ASU.

I have questions related to financial engineering on a topic other than what is listed here. Can you please provide me your email or anything else where I can address it.

Thanks.

Babu C Kumaran

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