Basic: Accrued Interest

[Giugio]

Hi all,

this is my first post, so let me say hello to everyone.

I've got a little of confusion about dirty price/clean price and accrued interest.
I know the definition and the basic relationship:

Clean Price = Dirty Price - Accrued Interest

But trying to calculate them on a spreadsheet it gives me slight differences when trying to calculate the Clean price by this relationship and the value calculate with pricing the cashflows.

Attached is the example. Really should be something easy, but to me is correct.

Could you please help me to understand what the difference is?

This is the example in text:

2.1 Bond with Accrued Interest

Face Value 100
Annual Coupon 10%
Discount Yield 6,5%
Redemption 100
Payment Freq 2

Settlement 01/06/06
Maturity 01/03/12

a. Day Count

Next Coupon 01/09/06
Days to Coupon 0,5000

b. Pricing ( Dirty )

Period Discounted
0,5000 4,92
1,5000 4,77
2,5000 4,62
3,5000 4,47
4,5000 4,33
5,5000 4,19
6,5000 4,06
7,5000 3,93
8,5000 3,81
9,5000 3,69
10,5000 3,57
11,5000 72,69
119,05

c. Accrued Interest

Previous Coupon 01/03/06
Day Count 0,5000
Accrued Interest 2,50

d. Clean Price 116,55

d2. Pricing ( Clean )

Period Discounted
1 4,84
2 4,69
3 4,54
4 4,40
5 4,26
6 4,13
7 4,00
8 3,87
9 3,75
10 3,63
11 3,52
12 71,53
117,16 <- Different from 116,55

 

[aaronhotchner]

I think you're really overcomplicating this. Discount future cash flows to get the clean price, and simply add imputed interest to get the dirty price. Your dirty and clean price calculations both have 12 payments occurring at different times; that is not how bonds are priced. All of the cash flows occur at the same time. The only difference is whether you count the back interest.

 

[aaronhotchner]

Looking at it a little more closely, I think I can better explain what's going on.

You are pricing the bond at two different time periods. For the dirty price, you recognize that cash flows occur in 3 months, 9 months, 15 months, and so on, so every 0.5 + x period of 6 months. In the clean price, you use integer periods starting at 1, so you're effectively pricing the bond as of the settlement date 6/1/2006 and assuming cash flows are 12/1/2006, 6/1/2007, and so on.