An investment company offers put options on a stock with exercise date t=1.

(a) 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=1. [3p] Suppose the (t=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. [4p]

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 t=1. [3p]