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quanteric
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Joined: June 4th, 2010, 12:01 am

Bond yield<->price calculation in the presence of stubs

October 20th, 2015, 2:38 pm

Hi, I am wondering if anyone is familiar with the calculation of bond yield/price under the usual "street" convention when there are stubs? Say if there is a short first coupon? I tried matching Bloomberg but could not quite match it exactly... Say if the next coupon date t2 is the stub payment, and today's date is t1. I first value the bond on date t2 as theres no stub then and the calculation would be as per usual. I then add the stub payment to get value x at time t2, and then i discount back to time t1 via x2/(1+y)^m where y is the yield and m is the dayount from t1 to t2. Is this how the stub is handled? Thanks very much for your help on this.
 
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mtsm
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Joined: July 28th, 2010, 1:40 pm

Bond yield<->price calculation in the presence of stubs

October 20th, 2015, 4:09 pm

In my understanding the yield to maturity is computed from the clean price of the bond, which is just the PV of all future cashflows. How you get that PV maybe subject to certain specificities. Stub or not doesn't matter does it? As long as you know the coupon rate and the day count with convention, you know the forward value of the cashflow. Just wanted to add that you should probably read the BBG help documentation on the topic. It is quite helpful.
Last edited by mtsm on October 19th, 2015, 10:00 pm, edited 1 time in total.
 
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Jim
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Joined: February 1st, 2002, 5:20 pm

Bond yield<->price calculation in the presence of stubs

October 20th, 2015, 4:13 pm

Excel's function wizard has reasonably good formulae for the price/yield functions. Open Excel, bring up the function wizard for, say, ODDLYIELD (yield with odd last period), and click on the "Help on this Function" link in the lower left of the dialog box. The online help give the formula by which the function is calculated.
 
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DavidJN
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Joined: July 14th, 2002, 3:00 am

Bond yield<->price calculation in the presence of stubs

October 22nd, 2015, 5:12 pm

Jim's suggestion is a good one. The Excel ODDYIELD formula seems to be a correct, if slow, implementation of the SIA Manual formula. (SIA = Securities Industry Association). Get a hold of that old book by Jan Mayle from a library and you will also find worked examples in it. Old fashioned yield-to-maturity bond math can be a bit harder than it looks. Consider, for example, that there are actually corporates and even agencies out there that are stupid enough to have issued bonds with odd first AND last coupons.