The current spot exchange rate is AUD 1.00 = USD 0.80. The Australian risk-free rate is 3.0%p.a. compounded continuously, whereas the US risk-free rate is 0.8% p.a. compoundedcontinuously. The no-arbitrage price on a 9-month forward contract written on the exchangerate is likely to bea) USD 0.813 / AUDb) AUD 0.787 / USDc) AUD 1.271 / USDd) AUD 1.230 / USD
Question
The current spot exchange rate is AUD 1.00 = USD 0.80. The Australian risk-free rate is 3.0%p.a. compounded continuously, whereas the US risk-free rate is 0.8% p.a. compoundedcontinuously. The no-arbitrage price on a 9-month forward contract written on the exchangerate is likely to bea) USD 0.813 / AUDb) AUD 0.787 / USDc) AUD 1.271 / USDd) AUD 1.230 / USD
Solution
To answer this question, we need to use the formula for the forward exchange rate in terms of the spot exchange rate and the interest rates of the two countries. The formula is:
F = S * e^(r_domestic - r_foreign) * T
where: F is the forward exchange rate S is the spot exchange rate e is the base of the natural logarithm (approximately equal to 2.71828) r_domestic is the domestic risk-free interest rate r_foreign is the foreign risk-free interest rate T is the time to the delivery date, in years
Given that: S = 0.80 USD/AUD r_domestic (Australia) = 3.0% per annum r_foreign (US) = 0.8% per annum T = 9/12 years
We can substitute these values into the formula to get:
F = 0.80 * e^(0.03 - 0.008) * (9/12)
After calculating, we get:
F = 0.80 * e^(0.022) * 0.75
F = 0.80 * 1.0223 * 0.75
F = 0.6137 USD/AUD
This is not an option in the given choices. There might be a mistake in the question or the provided options.
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