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slops
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Method to calculate effective interest of a bond price

May 29th, 2012, 8:09 pm

I have two different methods to calculate an effective interest that reflects a bond price. The methods are very similar indeed and the differences are only visible when looking into details such as method of day count conventions.My problem is that I should choose ONE method to implement in a financial system, but I have a hard time in finding what method the banks use.Example: Consider a bond with cash flows (amount, date) on date d1 we invest -N * price (price = market rate = e.g. 99.5 ) on date d2 we receive C on date d3 we receive C on date d4 the bond matures and we receive C+NWe now look for an effective interest rate R that reflects the bond.Method 11. Calculate the forward value of the amounts to d4, sum them and discount the sum to d1, i.e. Result = df(d1,d4) * ( C / df(d2,d4) + C / df(d3,d4) + C + N) (Here df are discount factors with respect to the effective interest rate R, e.g. df(d1,d4) = (1+R%)^(- (d4 - d1 )/365) in say Act /365 ) 2. Solve the equation Result / N = pricewith respect to R.Method 21. Discount each cash flow to d1 and sum Result = C * df(d1,d2) + C * df(d1,d3) + (C + N) * df(d1,d4) (As before, df are discount factors with respect to the effective interest rate R, e.g. df(d1,d4) = (1+R%)^(- (d4 - d1 )/365) in say Act /365 ) 2. Solve the equation Result / N = pricewith respect to R.One might argue that this results in the same thing, but it does not! If we consider Act/Act, then the day count fraction has 365 in the denominator provided the interest period does not contain a leap day and 366 otherwise - hence they may not cancel.References or comments are greatly appreciated. rrr
 
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slops
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Method to calculate effective interest of a bond price

May 30th, 2012, 9:15 am

No comment? Nothing?
 
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daveangel
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Method to calculate effective interest of a bond price

May 30th, 2012, 9:24 am

how is this different from calculating the yield on a bond or its IRR ?
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slops
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Method to calculate effective interest of a bond price

May 30th, 2012, 9:53 am

Daveangel, thanks for seeing me!You are right that is the same thing! I am just wondering which method is to prefer and what is standard among the banks. In our system we use Method 1 today, but I think method 2 is more straight forward - but then again, I don't know if there is a convention on this...
 
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daveangel
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Method to calculate effective interest of a bond price

May 30th, 2012, 10:07 am

do you forward and discount at the same rate in method 1 ?
knowledge comes, wisdom lingers
 
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slops
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Method to calculate effective interest of a bond price

May 30th, 2012, 10:08 am

Yes, I do.
 
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daveangel
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Method to calculate effective interest of a bond price

May 30th, 2012, 10:10 am

why do you think then that there should be a difference ?
knowledge comes, wisdom lingers
 
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slops
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Method to calculate effective interest of a bond price

May 30th, 2012, 10:17 am

For one thing, if I work in Act/Act and a leap day close to maturity say, then the day count quotient is 366 in all forward and discount calculations in Method 1 while for Method 2 it is 365 for all discounts except for the final settlement.I checked an example where the effective interest differed on the 3d decimal.