Explanation

This is a currency option pricing problem that can be solved using the Garman-Kohlhagen model (an extension of the Black-Scholes model for currency options).

Given parameters:

• Current spot rate (S) = $1.34/EUR
• Strike price (K) = $1.40/EUR
• Time to expiration (T) = 1 year
• Domestic risk-free rate (r_d) = 4% (US rate)
• Foreign risk-free rate (r_f) = 3% (Eurozone rate)
• Volatility (σ) = 30%

Garman-Kohlhagen formula for currency call option: $C = Se^{-r_fT}N(d_1) - Ke^{-r_dT}N(d_2)$

Where: $d_1 = \frac{\ln(S/K) + (r_d - r_f + \sigma^2/2)T}{\sigma\sqrt{T}}$ $d_2 = d_1 - \sigma\sqrt{T}$

Calculations:

1. $d_1 = \frac{\ln(1.34/1.40) + (0.04 - 0.03 + 0.3^2/2) \times 1}{0.3 \times \sqrt{1}} = \frac{-0.0435 + (0.01 + 0.045)}{0.3} = \frac{0.0115}{0.3} = 0.0383$

2. $d_2 = 0.0383 - 0.3 = -0.2617$

3. $N(d_1) = N(0.0383) ≈ 0.5153$ $N(d_2) = N(-0.2617) ≈ 0.3968$

4. $C = 1.34 \times e^{-0.03} \times 0.5153 - 1.40 \times e^{-0.04} \times 0.3968$ $C = 1.34 \times 0.9704 \times 0.5153 - 1.40 \times 0.9608 \times 0.3968$ $C = 0.670 - 0.534 = 0.136$

Therefore, the price of the call option is $0.136, which corresponds to option A.

Key insights:

• The option is out-of-the-money (spot < strike)
• The domestic rate (r_d) is higher than the foreign rate (r_f), which affects the forward price
• The volatility is relatively high at 30%, but the deep out-of-the-money position keeps the premium low