Suppose that a 6-month European call A option on a stock with a strike price of $75 costs $5 and is held until maturity, and 6-month European call B option on a stock with a strike price of $80 costs $3 and is held until maturity. The underlying stock price is $73 with a volatility of 15%. Risk-free interest rates (all maturities) are 10% per annum with continuous compounding.

(a) Construct a butterfly spread with the two kinds of options. Draw a diagram showing how the profit and loss of the trading strategy portfolio depends on the stock price at the maturity of the option.

(b) Use put-call parity to explain how would you construct a European put with the same maturity and strike price as European call A option. What is the price of the synthetic put?

(c) Suppose now the European call B option is dividend-paying with dividend yield 5% per annum. Use a two-step tree to value European call B. Draw the binomial tree and analyze. Specify the the percentage up move- ment, the percentage down movement, the risk-neutral probability of an up movement and a down movement.