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Answer: CNY 0.1171
A is correct. The following information has been given: S = current exchange rate = 6.7355 K = strike price of the option = 6.8665 r = risk-free interest rate in China (domestic) = 1.75% rf = risk-free interest rate in the US (foreign) = 3.25% At=0.5years u = upward move in exchange rate = 1.0582 d = downward move in exchange rate = 0.9450 An option to buy a foreign currency (in this case, UsD) can be considered an option to buy an asset providing a yield at the foreign (Us) risk-free rate. Therefore, the risk-neutral probability of an up move, p, is: \[ p = \frac{e^{(r - rf) \cdot t} - d}{u - d} = \frac{e^{(0.0175-0.0325) \cdot 0.5} - 0.9450}{1.05820.9450} = 0.4199 \] Thus, \( 1 - p = 1 - 0.4199 = 0.4008 = 0.5801 \) The two-step binomial tree for values of the exchange rate is shown below (multiplying by u for each up move and d for each down move):
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A Chinese investor wishes to acquire a 1-year European-style currency option to purchase USD. The current exchange rate is CNY 6.7355 per USD. A currency trader uses a two-step binomial tree model to price this option. The following details are provided:
Determine the value of the option to purchase one USD, given the current spot exchange rate.
A
CNY 0.1171
B
CNY 0.2792
C
CNY0.2813
D
CNY 0.6758
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