Hi all,
There's something that I just can't make sense of and would appreciate some help.
When calulating the conversion factor for a Treasury Bond Future, we round down the maturty date to the nearest 3 months period. So we can have the situation where there is an extra 3 months when we semi annualize the bonds present value.
Now the example in Hull is confusing me. I've attached a spreadsheet that shows the present value of the bond. This is in cells M26
61 on sheet1. I've scanned in the formula that hull uses from his book and placed it on the sheet. Both prices are the values of $125.83
However, the things I don't understand are:
1. The pricing of the bond, according to the Hull text, is to 3 months time. I believe that the bond is actually calculated to discount to the present time not 3 months!
For example the 1st coupon payment is worked out to be discounted to a factor 0.9708 for a 0.5 period to the present day.
4, 0.5, 0.970873786, 3.883495146
How can Hull work this out to be 3 months??
Surely the 1st time period used for calculating the price would be 0.25 - i.e. 3 months (0.25). This would yield a different price.
2. If you look at the formula scanned in the spreadsheet, he deals with the extra 3 months coupon by simply adding the a coupon payment of 4. How on earth does that add up? Wouldn't the extra 3 months 'at the maturity' of the bond need to be discounted back to a price today?? How can you just add an additional coupon payment not pv'ed or anything.
I can't make head or tails of this.
Any help is really appreciated
Thanks in advance,
Paul
There's something that I just can't make sense of and would appreciate some help.
When calulating the conversion factor for a Treasury Bond Future, we round down the maturty date to the nearest 3 months period. So we can have the situation where there is an extra 3 months when we semi annualize the bonds present value.
Now the example in Hull is confusing me. I've attached a spreadsheet that shows the present value of the bond. This is in cells M26
61 on sheet1. I've scanned in the formula that hull uses from his book and placed it on the sheet. Both prices are the values of $125.83However, the things I don't understand are:
1. The pricing of the bond, according to the Hull text, is to 3 months time. I believe that the bond is actually calculated to discount to the present time not 3 months!
For example the 1st coupon payment is worked out to be discounted to a factor 0.9708 for a 0.5 period to the present day.
4, 0.5, 0.970873786, 3.883495146
How can Hull work this out to be 3 months??
Surely the 1st time period used for calculating the price would be 0.25 - i.e. 3 months (0.25). This would yield a different price.
2. If you look at the formula scanned in the spreadsheet, he deals with the extra 3 months coupon by simply adding the a coupon payment of 4. How on earth does that add up? Wouldn't the extra 3 months 'at the maturity' of the bond need to be discounted back to a price today?? How can you just add an additional coupon payment not pv'ed or anything.
I can't make head or tails of this.
Any help is really appreciated
Thanks in advance,
Paul
