triangulated-fx-rates

1# Triangulated FX rates
2 
3Most rate feeds list a direct rate to the reporting currency (typically
4USD). Less liquid currencies are often quoted *through* a more liquid
5vehicle currency (commonly EUR or USD itself). On a batch rate tape this is
6encoded as a second "via" column on the same row:
7 
8```
9CCY  RATE     VIA
10USD  1.0000
11EUR  1.0850
12GBP  1.2750
13CHF  0.9200   EUR     <-- CHF -> EUR is the first hop
14ZAR  0.0650   EUR     <-- ZAR -> EUR is the first hop
15BRL  0.3000   ZAR     <-- BRL -> ZAR -> EUR -> USD : TWO via hops
16JPY  0.0064
17```
18 
19A blank `VIA` column means the row is already a direct quote against the
20reporting currency. A non-blank `VIA` column means the row gives the rate
21from CCY to VIA — and you still need to convert from VIA to the reporting
22currency.
23 
24## The via chain can be longer than one hop
25 
26This is the part that is easy to get wrong. The via currency named on a row
27is **not guaranteed to be a direct quote** — it may have its own non-blank
28via column, which in turn may have another, and so on. A single via lookup
29is therefore only correct when the via happens to be direct. To get a
30correct effective rate you must **follow the chain**: keep multiplying in the
31next leg's primary rate, moving to that leg's via, until you reach a row
32whose via is blank (a true direct quote against the reporting currency).
33 
34```
35effective_rate(CCY) = primary(CCY) × primary(via(CCY)) × primary(via(via(CCY))) × …
36…