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