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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
[my take]
Lower bound of a European put: P >= Max(Ke-rt - S0, 0)
What part of the wording gives away the point that the USD rate enters into the calculation? I mean, this information could be extraneous/trick so that we would discard it. Then P>= .688e(-.045*5/12) - .665 = .01022 (not in the answer set so it is obviously wrong)
Furthermore, I am not sure why the rates are placed in the calculation as such. Again other than the fact that this does not lead to an answer choice I am not clear. Would anyone have a reading resource for this? I think that in an exam setting I probably would not have discounted S and so I'm not clear about this question. Any help appreciated.
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
[my take]
Lower bound of a European put: P >= Max(Ke-rt - S0, 0)
What part of the wording gives away the point that the USD rate enters into the calculation? I mean, this information could be extraneous/trick so that we would discard it. Then P>= .688e(-.045*5/12) - .665 = .01022 (not in the answer set so it is obviously wrong)
Furthermore, I am not sure why the rates are placed in the calculation as such. Again other than the fact that this does not lead to an answer choice I am not clear. Would anyone have a reading resource for this? I think that in an exam setting I probably would not have discounted S and so I'm not clear about this question. Any help appreciated.
