a) Suppose that European put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. Assume that you buy one put with strike of $30 and sell one put with strike of $35 (bull spread). Sketch the graph and write down functions of payoff and profit. b) Assume that you buy one put with strike of $35 and sell one put with strike of $30 from point a) (bear spread). Sketch the graph and write down functions of payoff and profit. c) Three European put options on a stock have the same expiration date and strike prices of $55, $60 and $65. The market prices are $3, $5 and $8, respectively. Assume that you buy a put with lowest strike price and one with highest strike price and sell two puts with intermediate strike price (butterfly strategy). Sketch the graph and write down functions of payoff and profit