Answer: $0.136

## Explanation This is a currency option pricing problem using the Garman-Kohlhagen model (extension of Black-Scholes for currencies). The formula for a European call option on a currency is: \[ C = S_0 e^{-r_f T} N(d_1) - K e^{-r_d T} N(d_2) \] Where: - \( S_0 = 1.34 \) (current exchange rate) - \( K = 1.40 \) (strike price) - \( T = 1 \) (1 year) - \( r_d = 0.04 \) (domestic risk-free rate - USD) - \( r_f = 0.03 \) (foreign risk-free rate - EUR) - \( \sigma = 0.30 \) (volatility) Calculate \( d_1 \) and \( d_2 \): \[ d_1 = \frac{\ln(S_0/K) + (r_d - r_f + \sigma^2/2)T}{\sigma\sqrt{T}} = \frac{\ln(1.34/1.40) + (0.04 - 0.03 + 0.30^2/2) \times 1}{0.30 \times \sqrt{1}} \] \[ d_1 = \frac{-0.0435 + (0.01 + 0.045) \times 1}{0.30} = \frac{-0.0435 + 0.055}{0.30} = \frac{0.0115}{0.30} = 0.0383 \] \[ d_2 = d_1 - \sigma\sqrt{T} = 0.0383 - 0.30 = -0.2617 \] Calculate normal CDF values: - \( N(d_1) = N(0.0383) \approx 0.5153 \) - \( N(d_2) = N(-0.2617) \approx 0.3968 \) Compute the call price: \[ C = 1.34 \times e^{-0.03 \times 1} \times 0.5153 - 1.40 \times e^{-0.04 \times 1} \times 0.3968 \] \[ C = 1.34 \times 0.9704 \times 0.5153 - 1.40 \times 0.9608 \times 0.3968 \] \[ C = 0.670 - 0.533 = 0.137 \] The price is approximately $0.136, which matches Option A.

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