Todays price of the Apple Inc. (AAPL) stock is S0 $175. An investor instructs a broker to sell 100 European call options (= 1 call option contract) as well as 100 European put options (= 1 put option contract) written on Apple stock with a strike price of K $175 and maturity T on September 16, 2022 (that is, in exactly four weeks). The European call options are currently trading for $5.00 per option and the European put options are currently trading for $4.50 per option. (a) What is the payoff function of the investors position at maturity T as a function of the then prevailing Apple stock price ST ? Sketch the graph of the function and add suitable annotations. (b) What is the profit and loss of the investors position at maturity T as a function of the then prevailing Apple stock price ST ? Sketch the graph of the function and add suitable annotations. (c) What is the maximum possible profit and what is the maximum possible loss for the investor at maturity T? (d) For which stock prices ST does the investor make a strictly positive profit? (e) What is the investor speculating on with her option strategy?

1. (10 points) Today's price of the Apple Inc. (AAPL) stock is S0=$175. An investor instructs a broker to sell 100 European call options ( =1 call option contract) as well as 100 European put options (=1 put option contract) written on Apple stock with a strike price of K=$175 and maturity T on September 16, 2022 (that is, in exactly four weeks). The European call options are currently trading for $5.00 per option and the European put options are currently trading for $4.50 per option. (a) What is the payoff function of the investor's position at maturity T as a function of the then prevailing Apple stock price ST ? Sketch the graph of the function and add suitable annotations. (b) What is the profit and loss of the investor's position at maturity T as a function of the then prevailing Apple stock price ST ? Sketch the graph of the function and add suitable annotations. (c) What is the maximum possible profit and what is the maximum possible loss for the investor at maturity T ? (d) For which stock prices ST does the investor make a strictly positive profit? (e) What is the investor speculating on with her option strategy