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Lower Bound of Euopean Currency Put RSS

chunleeng

Posted: 17 November 2009 03:21 AM   [ Ignore ]
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Hi David,

Fr 2003 FRM exam,
-Current USD/AUD rate is 0.6650
-USD riskfree rate is 1%
-AUD riskfree rate is 4.5%
What is the lower bound of a 5 mth European put option on the AUD with a strike price of 0.6880?

Answer:
Lower bound = Xe^(-USD rf x 5/12)  - Se^(-AUDRF x 5/12)
Lower bound = 0.6880xEXP(-0.01*5/12) - 0.6650xEXP(-0.045*5/12) = 0.0325

My confusions:
1) Why it is different with p>= max(Ke ^ -rT - S0, 0)?
2) Could we adjust the strike price and then minus the current exchange rate?  0.6880exp(-(0.01-0.045)*5/12) - 0.665
3) Could we use strike exchange rate minus the calculate the forward exchange rate? 0.6880 - 0.6650 exp(-(0.01-0.045)*5/12)

Your advice, please.

Thanks
Learning

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David Harper, CFA, FRM, CIPM

Posted: 17 November 2009 12:16 PM   [ Ignore ]   [ # 1 ]
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Hi Learning

The foreign currency (AUD) is treated like dividend yield (as in interest rate parity).
So it is it different than this: p>= max(Ke ^ -rT - S0, 0)
...because that assumes dividend yield = 0

if we converted the AUD rate (4.5) to its equivalent lump sum:
spot*(1-exp(-qT) = D
in this case, D = 0.012353 = 0.665*(1-exp(-4.5%*5/12)
...all i did there was convert a 4.5% constand “dividend” (foreign rate) into a lump sum dividend

then we could apply Hull 9.6:
p >= K*exp(-rT) - S0 + D
here: p>= 0.688*exp(1%*5/12) - 0.665 + 0.012353 = 0.032492; i.e., same result
...so that essentially converst the strike price

I am not sure about a third way…

David

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