
Financial Risk Manager Part 1
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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:
- Option expiration time: 12 months
- Option strike price: CNY 6.8665 per USD
- China's annual continuously compounded risk-free interest rate: 1.75%
- US's annual continuously compounded risk-free interest rate: 3.25%
- Exchange rate increase factor: 1.0582
- Exchange rate decrease factor: 0.9450
Determine the value of the option to purchase one USD, given the current spot exchange rate.
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:
- Option expiration time: 12 months
- Option strike price: CNY 6.8665 per USD
- China's annual continuously compounded risk-free interest rate: 1.75%
- US's annual continuously compounded risk-free interest rate: 3.25%
- Exchange rate increase factor: 1.0582
- Exchange rate decrease factor: 0.9450
Determine the value of the option to purchase one USD, given the current spot exchange rate.
Explanation:
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: Thus, 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):