Question: We use binomial trees to value American-style options on the British pound. Assume that the British pound is currently worth $1.40. Volatility is 20%. The current British risk-free rate is 6% and the US risk-free rate is 3%. The put option has a strike price of $1.50. It expires in 200 days.
a. The first issue to be settled is the role of US and British interest rates. This option is being purchased in the United States, so the relevant risk-free rate is 3%. But British pounds can be used to earn the British risk-free rate. So this variable can be treated as a continuous rate of dividends. Or we can say that interest rate differentials are supposed to equal the expected appreciation of the currency. Taking this into account, determine a Δ such that the binomial tree has five periods.
b. Determine the implied u and d and the relevant probabilities.
c. Determine the tree for the exchange rate.
d. Determine the tree for a European put with the same characteristics.
e. Determine the price of an American-style put with the previously stated properties.