1. (10 points) Today the price of Apple Inc. stock (AAPL) is $180 per share. A trader buys one put option contract on 100 AAPL shares with a strike price of K2=$180 and sells one put option contract on 100AAPL shares with a strike price of K1=$160. Both options have the same maturity date T, which is September 8 (i.e., in two weeks). The market prices of the options are $2.20 (for K2=$180 ) and $0.10 (for K1=$160 ), which are quoted per share. (a) Provide the final payoff function at maturity T of the trader's combined position as a function of the then prevailing stock price ST. Sketch the graph and add suitable annotations. (b) Provide the profit and loss at maturity T of the trader's combined position as a function of the then prevailing stock price ST. Sketch the graph and add suitable annotations. (c) What is the maximum possible profit and what is the maximum possible loss for the trader at maturity T ? (d) For which range of stock prices ST does the trader make a strictly positive profit? (e) What is the trader speculating on with her option strategy