Use the binomial tree technique to price a one year American call option with strike price $65, written on a $60 stock. Use a two step tree, with 6 month time steps. Volatility is 18%. The stock will pay a dividend in 7 months time of $4. Interest rates are 7%, with continuous compounding. 2. Price a 6 month European put option with strike price $NZ1.30, written on the US dollar. The current exchange rate is $NZ1.40=$US1.00. Volatility is 14%, the NZ dollar interest rate is 7.5%, and the US dollar interest rate is 5.8% (both with continuous compounding). Use the Black-Scholes formula. 3. Suppose you had written the US dollar option from the previous question. You now need to hedge the option, and in order to do so, have decided to calculate Delta (), Gamma () and Theta (). (a) Calculate the three quantities using the finite difference technique, using of 0.001. Hint: This may be done quite quickly in excel. (b) Now compare your solutions to the results from the formulae in the textbook/notes.