Serving the Quantitative Finance Community

 
User avatar
dimitri
Topic Author
Posts: 0
Joined: July 14th, 2002, 3:00 am

Business day adjustment on accrued interest

July 28th, 2006, 10:02 am

I have some problems calculation year fraction and Accrued Interest, and how business day adjustment should be taken into account.Let’s take the DayCount problem first. I want to calculate the yearfrac for a money market paper from 1-jan-2006 to 1-apr-2006, using act/360. Will I have to adjust to the correct business dates before I calculate the act part?2-jan-2006 to 3-apr-2006 = 91or do I calculate from 1-jan-2006 to 1-apr-2006 (= 90 days)?The second question is about accrued interest. I want to calculate accrued in-terest rate for a bond using act/act ISMA, on the same period as before. Lets say the tradedate is 7-feb-2006 and the settlement date is then 10-feb-2006. From which dates should I then calculate the “number of days” part1-jan-2006 to 10-feb-2006 = 40 / 90Or is it2-jan-2006 to 10-feb-2006 = 39 / 91Hope someone can help me on this question, since I can’t find any literature on this subject.
 
User avatar
cemil

Business day adjustment on accrued interest

July 28th, 2006, 11:35 am

Dimitri,1. As the 1st january is not a business day, the deal will be made on the 2nd january and will be end at the 3rd april.2. For the bond it is different, firstly you need the feature of the bond (Maturity, coupon frequency, coupon adjusted or not....).Suppose, The bond coupon date is 1st january with a yearly coupon frequency so: Accrued coupon=(10-feb-2006 - 1-jan-2006 )/365
 
User avatar
cemil

Business day adjustment on accrued interest

July 28th, 2006, 11:37 am

Dimitri,1. As the 1st january is not a business day, the deal will be made on the 2nd january and will be end at the 3rd april.2. For the bond it is different, firstly you need the feature of the bond (Maturity, coupon frequency, coupon adjusted or not....).Suppose, The bond coupon date is 1st january with a yearly coupon frequency so: Accrued coupon=(10-feb-2006 - 1-jan-2006 )/365 =40/365 = 0.1095
 
User avatar
dimitri
Topic Author
Posts: 0
Joined: July 14th, 2002, 3:00 am

Business day adjustment on accrued interest

July 28th, 2006, 11:53 am

For the Accrued interest I’m only interested in the yearfrac part. I assumed that the coupon frequency is quarterly, so according to the act/act ISMA the yearfrac should be calculated as(10-feb-2006 - 1-jan-2006 ) / ((1-apr-2006 – 1-jan-2006) * PayFreq) = 40 / (90*4) = 0,111111The thing I wasn’t so sure about was if I should adjust the dates to business dates as I’m doing when I’m calculating the yearfrac in the first question.
 
User avatar
cemil

Business day adjustment on accrued interest

July 28th, 2006, 12:05 pm

Even if you are only interested on the "yearfrac", you have to know the maturity of the bond :-)Give me a maturity and I will show you how to calculte it (quaterly)
 
User avatar
cemil

Business day adjustment on accrued interest

July 28th, 2006, 12:08 pm

If we suppose the maturity of the coupon date is 1 january then you calculation is right
 
User avatar
dimitri
Topic Author
Posts: 0
Joined: July 14th, 2002, 3:00 am

Business day adjustment on accrued interest

July 28th, 2006, 12:14 pm

Let’s say the bond has coupon payments 1-jan-2006, 1-apr-2006, 1-jnu-2006 ... until 1-1-2010 and the couponrate is 5%.
 
User avatar
cemil

Business day adjustment on accrued interest

July 28th, 2006, 12:33 pm

Your calculation is right. And the formula is (for the yearfrac):(settle - previous coupon date) / (next coupon date - previous coupon date)/Coupon frequencyBut be carefull about the calculation of accrued coupon, each country have different way to calculate the accrude value.
 
User avatar
dimitri
Topic Author
Posts: 0
Joined: July 14th, 2002, 3:00 am

Business day adjustment on accrued interest

July 28th, 2006, 3:40 pm

Cemil, I appreciate your help and I know that I have to be careful. I’m trying to implement a lot of different DayCount convention, and it is hard to find any literature, with some good examples.If it was a money market paper with the same kind of cashflow, would I calculate the accrued interest rate in the same way as for the bond?And is it correct that when I’m calculating the yearfraction used for the coupon payment (cashflow), then I will always have to adjust it to a business date no mater if it is the money market or the bond market?