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What are those five date maturity ranges?

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For fixed income instruments, the maturity can be entered as either a single value (like 10, for ten years, or 12/12/09 for December 12, 2009) or a five element range (5 cells in Excel, where each one is either a term or a date). When it's a single number, things are pretty self-explanatory: TOPS uses that date, and the frequency, to back out a series of dates between the valuation date and the maturity date. But if there are odd periods, entering a single maturity won't do, and that's where the five cell range comes in.


The meaning of the five cells are:


start of first period (the effective date)

end of first period (the first payment date)

start of last period

end of last period (the maturity date)

roll date


In this way, it's fairly simple to enter a long or short first period, and a long or short last period, or both, by setting the first four dates appropriately. So what's the roll date for? A few things:


1) if the first or last period is odd, it allows you to tell TOPS whether the rolling of dates in betwen the first and last period go from the start date or the end date of the period. For example, suppose the effective date is January 15, and the first payment date is March 15. Should a quarterly roll be in January or March? What if the last period of the same deal goes from June 10 to October 12? The roll date is totally ambiguous in that case. So by entering a fifth date, the ambiguity is resolved.


2) The roll date of the previous example could be none of the four other dates, say March 20. That would allow for an odd first period, and odd second period, an odd last period, and an odd second to last period. A strange structure, to be sure, but nonetheless possible.


3) Telling TOPS whether observations occur multiple times in one payment period. If the first period is long, say semi-annual, with semi payments, and the observations are quarterly, should there be two observations in the first period (effective date, and three months later), or one (on the effective date)? By setting the roll date to the effective date, two observation dates will be generated. Setting the roll date to the first payment date will cause TOPS to generate just a single observtion date on the effective date.


To help clarify this, here's a rough outline of the algorithm TOPS uses to generate dates:


1) Insert all 5 dates in the list.


2) Determine if the roll date is closer to the first date (in which case we roll forward), or the fourth date (in which case we roll backwards).


3) Starting at the roll date, roll forwards or backwards based on the frequency (so if quarterly, roll 3 months at a time, etc.). Keep going until we are either after maturity (fourth date) when rolling forward or before effective (first date) when rolling backward.


4) Sort the dates


5) A boolean variable is passed into the routine to indicate if dates can be generated between the first and second dates, and between the third and fourth dates (the stub periods). If that variable is true, remove all dates before the first date and after the last date. If that variable is false, also remove any dates inside the stub periods (but not the stub period start and end dates that were aded in step 1).


6) Adjust all the dates for weekends (if weekends is set to no) and holidays.


7) Remove duplicates.


In reality, the removing of duplicates happens several times in the process; I'm not sure if it's necessary to do it before step 7, but we do.


The key here is that if the roll date is equal to the second date, then resets during the stub period will not be generated in step 3. Even if they are generated, if the boolean passed in is false, they'llbe correctly removed (for say the payment date scehdule) in step 5.

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