Garp 2006 practise question Q:90

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Q. If the current USD/AUD rate is 0.6650 (1 AUD=0.6650USD) and the risk-free rates for the
USD and AUD are 1.0% and 4.5% respectively, what is the lower bound of a 5-month European
put option on the AUD with a strike price of 0.6880?

a. 0.0135
b. 0.0245
c. 0.0325
d. 0.0455
ANSWER: C
The lower bound for a European option is given by the formula: Xe-rT - Se-rfT, where X
is the strike price, r is the risk-free rate of the USD, rf is the risk-free rate of the AUD,
T is the time to maturity and S is the spot rate of the AUD/USD.
Thus, the lower bound = 0.6880 x [exp-(0.01x 5/12)] – 0.6650 x [exp-(0.045x 5/12]]
= 0.6880 x (0.9958) –0.6650 x (0.9814)
= 0.6851 – 0.6526 = 0.0325

But my doubt is that formula for lower bound of European Put option is Xe-rT - So. Why they have calculated PV of So and made formula as Xe-rT - Se-rfT

 

[David Harper CFA FRM]

Hi snigdha,

The lower bound of a put with dividend is p>=K*EXP(-rT) - S*EXP(-qT), where the special case of non-dividend such that q = 0 gives: p>=K*EXP(-rT) - S

The general idea with foreign currencies is that the foreign interest rate is like a dividend yield; e.g., to a US investor (USD) the Canadian Dollar(AUD) is paying a "dividend yield" of 4.5%, so (r_foreign) replaces (q):
p>=K*EXP(-r_domestic*T) - S*EXP(-r_foreign*T)

David

 

[[email protected]]

Ohhh.. thats y I was wondering which one to take as q and which one as r...!!
My god... such small small technicalities and solid understanding is reqd..
Ur guidance is really very insightful...!!!

Thanks a lot.
BT rocks!!
-snigdha