Finance derivatives Need full answers thx.

1. a) A stock price is currently $30. The risk-free interest rate is 6.5% p.a. compounded semi-annually, and the dividend yield on the stock is 4% p.a. continuously compounded. The volatility of the stock price is 40% p.a. continuously compounded. Using the binomial option pricing model, what is the value of the 6-month American call option on the stock with a strike price of $20? You may assume there are two time steps of 3-months each. In providing your answer, be sure to include a diagram of the binomial tree with all nodes clearly labelled. (6 marks) 2. b) Suppose that the 9 month futures price on BHP Billiton is currently $34 per share, and the volatility of this futures contract is expected to be 23% p.a., continuously compounded. Further, the risk free rate of interest is currently 4.25% p.a. continuously compounded. Using the preceding information, complete the following: 1. Calculate the value of a 7-month European put futures option on BHP Billiton with a strike price of $42 per share; (3 Marks) II. Calculate the value of a 7-month European call futures option on BHP Billiton with a strike price of $22 per share; (3 Marks) 3. III. Calculate the bounds for an at-the-money 7-month American call futures option on BHP Billiton, when a 7-month American put futures option on BHP Billiton with the same strike price is selling for $3.20. (3 Marks) 1. a) A stock price is currently $30. The risk-free interest rate is 6.5% p.a. compounded semi-annually, and the dividend yield on the stock is 4% p.a. continuously compounded. The volatility of the stock price is 40% p.a. continuously compounded. Using the binomial option pricing model, what is the value of the 6-month American call option on the stock with a strike price of $20? You may assume there are two time steps of 3-months each. In providing your answer, be sure to include a diagram of the binomial tree with all nodes clearly labelled. (6 marks) 2. b) Suppose that the 9 month futures price on BHP Billiton is currently $34 per share, and the volatility of this futures contract is expected to be 23% p.a., continuously compounded. Further, the risk free rate of interest is currently 4.25% p.a. continuously compounded. Using the preceding information, complete the following: 1. Calculate the value of a 7-month European put futures option on BHP Billiton with a strike price of $42 per share; (3 Marks) II. Calculate the value of a 7-month European call futures option on BHP Billiton with a strike price of $22 per share; (3 Marks) 3. III. Calculate the bounds for an at-the-money 7-month American call futures option on BHP Billiton, when a 7-month American put futures option on BHP Billiton with the same strike price is selling for $3.20