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## Sunday, May 3, 2015

### Q: fxo premium as percentage of notional - mismatch!

There's an illustration in Tony's lecture notes and also in the homework -- 3 month 1.10 EUR call USD put, with Spot = 1.07
Assume the premium = 0.0200, given in USD per EUR
Then pnumccy = 0.0200, or a trader might say "200 USD pips"
"USD %" would be 0.0200/1.10 = 1.82%, pnumccy% = 0.0182
"EUR pips" would be 0.0182/1.07 = 0.0170 or "170 EUR pips"
"EUR %" would be 0.0200/1.07 = 1.87%, pbaseccy% = 0.0187

Observation -- last line 1.87% means the premium is 1.87% of the EUR notional; the 1.82% means the same premium is 1.82% of the USD notional.

The paradox -- the same premium is 1.87% of the EUR notional but only 1.82% of the USD notional !

(In general, paradoxes provide "aha" moments and great learning opportunity.)

Analysis (thin->thick->thin):

Key -- the USD notional and EUR notional can have (vastly) different values before maturity.

Let's focus on OTM (more common). Without loss of generality, let's consider deep OTM. In such a case the EUR notional is almost worthless and the USD notional is a king's ransom.

Naturally, the premium as percentage of the ransom is tiny.