You work for SABMiller plc in London. You have an accounts payable balance of 10 million Chinese new yuan (CNY) that is due in one year to a Chinese supplier. HSBC is offering a European call option on 10 million yuan with an exercise price of K£/CNY = £0.10/CNY. The current spot rate is S0£/CNY = £0.0940/CNY. You estimate that the standard deviation of continuously compounded returns to the St£/CNY exchange rate is σ = 20 percent per year. The continuously compounded risk-free rates of interest are iF£ = 2 percent in sterling and iFCNY = 3 percent in yuan.
a. How much would you be willing to pay for this call option assuming the Biger-Hull currency option pricing model is correct?
b. Holding everything else constant, would you be willing to pay more or less for this option given each of the following changes?
i) The exchange rate increases to £0.0950/CNY
ii) The exercise price is increased to K£/CNY = £0.11/CNY
iii) The risk-free rate increases to iF£ = 2.1 percent in sterling
iv) The risk-free rate increases to iFCNY = 3.1 percent in yuan
v) The time to expiration increases from one to two years
vi) Exchange rate volatility increases to σ = 40 percent per year.
Describe the intuition behind each of these effects on the value of the currency call option?
c. Repeat steps a and b for a put option on yuan.