help with all parts thanka

(a) Question 2 [10 points) An investment company offers put options on a stock with exercise date t=1. Draw the payoff (at t=1) of a portfolio that consists of the following two put options: Buy a put with exercise price E=$10 Sell a put with exercise price E=$20 as a function of the underlying stock price at t=l. (3p) Suppose the (+0) prices of these puts are as follows: Price E=$10 $3.00 E=$20 $2.00 (b) Is there an arbitrage? If so, find a profitable trading strategy. 14p) The investment company adds one more option to the above portfolio. (c) Draw the payoff (at t=1) of a portfolio that consists of the following three put options: Buy a put with exercise price E=$4 Buy a put with exercise price E=$10 Sell a put with exercise price E-$20 as a function of the underlying stock price at tel. (3p)