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4. A binomial tree with three-month time steps is used to value a currency option. The domestic and foreign risk-free rates are 2% and 4% respectively. The volatility of the exchange rate is 20%. What is the risk neutral probability of an up movement? What is the price of a six month European put option with a strike price of $1.01 when the exchange rate is $1.0? How would you hedge a long position in this option?

5. A futures price is currently 40 cents. It is expected to move up to 45 cents or down to 35 cents in the next six months. The risk-free interest rate is 5%. What is the probability of an up movement in a risk-neutral world? What is the value of a six month European put option on the futures struck at 39 cents. How would you hedge a long position in this option?