3. Calculate \( u, d \), and \( p \) when a binomial tree is constructed to value an option on a foreign currency. The tree step size is one month, the domestic interest rate is \( 5 \% \) per annum, the foreign interest rate is \( 8 \% \) per annum, and the volatility is \( 12 \% \) per annum. [4 Marks]
4. What is the difference between an American option and a European option? Under what circumstances would an investor consider an American option instead of a European option. [5 Marks]
5. A stock index is currently 1500 . Its volatility is \( 18 \% \). The risk-free rate is \( 4 \% \) per annum (Continuously compounded) for all maturities and the dividend yield on the index is \( 2.5 \% \). The price of a 12-month European put option with a strike price of 1480 is given by 87.3391 .
5.1 Calculate values for \( u, d \), and \( p \) when a six-month time step is used.
5.2 What is the value a 12-month American put option with a strike price of 1480 given by a two-step binomial tree.
5.3 Comment on the difference in the option prices.
5.4 One would expect that the price of the American option to be larger than that of its European counterpart. Comment on why this is not the case.
[21 Marks]
