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Subject: Re: [office-formula] euroconvert

On Wed, 2009-12-02 at 14:56 -0500, robert_weir@us.ibm.com wrote:
> "Andreas J. Guelzow" <aguelzow@math.concordia.ab.ca> wrote on 12/02/2009 
> 02:19:07 PM:
> > Is this function really just a synonym for multiplication with one of a
> > small selection of factors, or is in fact more happening here (such as
> > truncation or rounding of the result)?
> > 
> Certainly, there are very simple mathematical facts at the core of this 
> function: a list of a dozen conversion factors from legacy national 
> currencies to the Euro.  But the bankers made it a bit more complicated.
> The main complication is the EC's Rule 1103/97:  
> http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CELEX:31997R1103:EN:HTML
> Especially note Articles 4 and 5, where specific rules for rounding are 
> specified and what was later called the "triangulation rule" is specified 
> for conversion between legacy currencies using the Euro as a intermediary 
> format.  Now why this added complexity, you might ask?  I'm not sure, but 
> my guess is they wanted to publish a simple list of N conversion factors 
> and not an N^2 factors, some of which would be inexact, or favoring one 
> direction or another, introducing arbitrage opportunities, etc.  In any 
> case, the intent of this function is to implement the canonical conversion 
> from Rule 1103/97.  In fact, we should probably reference that Rule in the 
> definition of the function.

I do think we should be slightly more precise then the description goven
in the rule since it only specifies that (the euro amount) "may be
rounded to not less than three decimals" and even worse the rounding in
the national currency is "according to national law or practice".


Andreas J. Guelzow, PhD, FTICA
Mathematical & Computing Sciences
Concordia University College of Alberta

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