Financial Risk Manager Part 1

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.




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: p=e(rโˆ’rf)โ‹…tโˆ’duโˆ’d=e(0.0175โˆ’0.0325)โ‹…0.5โˆ’0.94501.05820.9450=0.4199p = \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, 1โˆ’p=1โˆ’0.4199=0.4008=0.58011 - 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):