currency option contracts

[Eveline]

Hi David,

I know it sounds a bit stupid but can you tell me whether the int rate here refers to the domestic int rate or the foreign int rate? How do you analyse this question? I got the answer right by pretending that the int rate is the dividend yield...

Assuming constant int rates, which of the folllowing American currency option contracts may be exercised prior to maturity of the option contract?
1) call option on high int rate currency
2) call option on low int rate currency
3) put option on high int rate currency
4) put option on low int rate currency

Ans: 1 and 4

Thanks!

 

[David Harper CFA FRM]

Hi Eveline

The "rate" in "high interest rate" currency refers here to the foreign rate ... although I do see your point about its ambiguity (there are two rates!) ... I guess it's the use of "option on a currency" that implies the foreign rate; i.e., the option is to buy a foreign currency so "option on a high rate" implies the rate of the foreign currency.

Otherwise, I am not convinced it's a good question...it comes straight from Hull, where, just as you say, we treat the foreign currency as equivalent to a dividend. So the intent of the question is based on IRP:

F = S*EXP(domestic rate - foreign rate); i.e., using foreign rate as dividend

where if foreign rate > domestic spot rate, we should have backwardation (inverted) forward curve with the high foreign rate implying that the foreign currency is expected to *depreciate* ...if that is too technical...

* if the foreign rate is high, how can the domestic currency compete? It must appreciate (as the currency investment will ~ equal the riskless rate + currency appreciation; e.g., USD rate = 4%, FX rate = 7%. Why wouldn't well all invest in FX? The USD must be expected to appreciate...
* or, if you just think about an option on a stock, the analogy is like:
F = S*EXP[4% riskless - 6% dividend];
i.e., if the dividend excess the rate of return, you must have capital depreciation or there is a "free lunch" (total gain = dividend + capital appreciation). If dividend yield exceed your total shareholder return, your must have capital depreciation.

so, if spot price exchange rate is $1.6 USD/1 unit foreign
...and high foreign domestic rate implies foreign currency depreciation
... then this implies the spot is not headed "up" to $1.8/fx but rather "down" to $1.4/fx
(i.e., $1.4 is depreciation from $1.6 b/c the 1 unit of foreign is buying fewer dollars)

so if you hold $1.6 and you are expecting foreign depreciation (i.e., USD appreciation), you are more likely to exercise an in the money call option. Time is against you for the call; conversely, "time is on your side" for a put: even if ITM, high foreign interest rate implies you should still hold onto the put.

Nonetheless, in my opinion, I think the question is flawed: I think a student of Hull could still equate the FX rate to dividends, just as you did, and then, given the question says "MAY be exercised prior..." may justifiably give an answer of: all of the above. Because we are talking about an option on dividend-paying stock, and it may always be optimal to early exercise the put and sometimes even the call....

David