Hi all,I have a question regarding how to deal with day count inconsistencies in a curve fitting setting. Suppose we have a bond maturing on 6/30/2015 for settlement on 6/1/2010. Then the exponents (T*2) in the standard bond pricing formula should be 29/181=0.1602, 1.1602, 2.1602, ... But for the time in years in the discount function d(t) seems to be 29/365=0.0794, 213/365=0.5836, 394/365=1.0794. Multiplying these numbers by 2 doesn't match the time factors previously calculated for the bond pricing formula. How should we deal with this?Thanks in advance!

Are you by chance refering to the regular settlement date on bonds regularly being later than the value date of your zero curve? Bonds sometimes take several days to settle whereas countries with sensible swap conventions (the UK, Canada, Australia etc.) have swap curve value dates equal to the trade date. Anyway, the quoted market price for your bond is based off one settlement convention and you will need to adjust your zero curve to meet that convention. In other words, you will likely have to convert your spot discount factors into (ever so slightly) forward discount factors to get consistent results.

Hi David,sorry but this is not my question. I'll try to make the question more concrete: suppose we have a 10% coupon bond maturing on 6/30/2015 for settlement on 6/1/2010. Using conventional bond pricing formula, the next cash flow $5, which occurs on 6/30/2010, will be discounted by (1+r/2)^(-29/181). My question is in a curve fitting setting, where the discount function is d(t), how should we express "t"? It makes sense to use 29/365, but of course 29/365*2 is not equal to 29/181.Just curious how professionals deal with this. Thanks!

haginileYou solve for the discount factors of the the instruments you are building your curve with, and express them consistently, ie make all semiannual or annual or whatever, and you're done. When you need to do pricing, interpolate the rate for that particular tenor, and then convert it back to the convention used for that particular instrument.All this works perfectly in an OOP framework where a fitted curve is an object, and there are methods to translate to whatever type of rate/discount factor you might need.

Ok. frattyquant has answered your question - count time in a way consistent with the day count and compounding frequency of your zero curve. The only things you need from the bond per se are the cash flows. But sooner or later you'll also have to get your head around the question I posed, unless by fluke the bond settlement dates are always the same as the value dates of your curves.