
Explanation:
According to the put-call parity for currencies, the relationship between a European call and put option is given by the formula: .
Given:
S = \`1.80$ $C = \
X = \`1.70$ $T = 1$ year $r = 5\%$ or (domestic risk-free rate)
or $0.08$ (foreign risk-free rate)
Substituting the values into the formula:
$0.135 - P = 1.80 \times e^{-0.08 \times 1} - 1.70 \times e^{-0.05 \times 1}0.135 - P = 1.80 \times 0.9231 - 1.70 \times 0.9512$
$0.135 - P = 0.0445P = 0.135 - 0.0445 = `
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Q.15 A foreign currency is valued at $1.80. The foreign currency has a European call option with a market price of $0.135, strike price of $1.70, and exactly one year to maturity. In the US, the risk-free interest rate is 5% per annum and 8% per annum in the foreign country. Assuming no arbitrage, determine the price of a European put option with a strike price of $1.70 and 1-year to maturity for the foreign currency. (Tip: Let the yield on the underlying stock be equal to the foreign risk-free rate.)
A
$0.254
B
$0.153
C
$2.5608
D
$0.0905