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YouTube TI BA II+: How to compute bond price on realistic (between coupons) settlement date (TIBA - 02)

Nicole Seaman

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This video will show you two different approaches to retrieving a bond's full and flat price when we have the realistic situation of a settlement date that occurs in between two coupon dates.

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Can I offer a small suggestion that might help newbies like myself? In the future, would you consider providing a link to calculator videos in the study notes? thanks! James

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David, I have a question concerning the use of the exponential function that is being used throughout the entire FRM course.
Taking say calculation of Forward Prices as an example ie F0 = S0erT, is the calculation of a forward price, ie there is not a negative value applied to the rT amount, that said a number of equations use a negative value when assigning to the calculation.
My understanding when you are attempting to calculate the present value you would use the negative value compared to say when calculating a forward price you dont use the negative function. Have I correctly summarised this or not, your clarification is appreciated. Thanks

David Harper CFA FRM

David Harper CFA FRM
Staff member
HI @Tim_Rogers The exp(rt) compounds forward over T years with continuous compounding. For example, $10.00 today (i.e., present value) grows at 7.0% per annum with continuous compounding over five (5) years to a future value of 10*exp(0.07*5) = $14.19. This is just the continuous analog to, say, semi-annual compounding which would produce a future value of 10*(1 + 0.07/2)^(5*2) = $14.11. If we take F0 = S0*exp(rt) and divide both sides by exp(rt), then we have solved for the current spot (i.e., present value) as a function of the future price: S0 = F0/exp(rt) = F0*exp(-rt) because 1/a^b = a^(-b) and 1/exp(a) = exp(-a). So if we want the present value of $10.00 to be received in five years, discounted at 7.0% per annum with continuous compounding, then the PV = 10/exp(0.07*5) = 10*exp(-0.07*5) = $7.05; and we could test it by compounding forward: $7.05*exp(0.07*5) = 10.00. And this is the continuous analog to, say, semi-annual discounting which would instead give us a PV = 10/(1+0.07/2)^(5*2) = 10*(1+0.07/2)^(-5*2) = 7.09. I hope that's helpful,