1. [25 points] The following table provided CALL and PUT options for Apple Inc. (AAPL) stock, which ended trading at US$1203 (-$0.93; -0.76%) on March 12, 2021 (at 4:00PM EST; at close). According to the listing, the options are going to expire on April 16, 2021 (i.e., it expires in 35 days). One option contract is equivalent to 100 shares.

CALL
	Option Price
Strike	Last Price	Bid	Ask	Change	% Change	Volume	Open Interest	Implied Volatility
120	5.59	5.55	5.7	-0.61	-9.84%	14,763	79,844	35.24%
125	3.35	3.35	3.4	-0.44	-11.61%	6,240	72,491	34.35%
PUT
Strike	Last Price	Bid	Ask	Change	% Change	Volume	Open Interest	Implied Volatility
120	4.55	4.5	4.55	0.4	9.64%	17,619	89,396	34.42%
125	7.28	7.2	7.3	0.53	7.85%	580	56,787	33.86%

Source: AAPL 121.03 -0.93 -0.76% : Apple Inc. - Yahoo Finance; NasdaqGS Real Time Price

1. Suppose you purchased the $125 CALL option contract written by one of your classmates. (Answer the following on a per contract basis.)
   1. What right does the option give you? At what cost per contract? What is the intrinsic value per contract of this option on March 12? What is the time value per contract of the option on March 12?
   2. What will happen if the price of Apple Inc. stock rises to $150 per share before April 16 and you decide to exercise your option?
   3. Will you make a profit or a loss on your contract when the stock price is $150? How much?
   4. Draw a diagram to show the pattern of profits or losses per share for your call option position. Label the diagram with all necessary information (Payoff, Profit, etc)
2. Suppose you purchase Apple Inc.s stock for $120 and a PUT option for $4.55 per share with a strike price of $120 per share. At the same time, you sell a call for $5.59 with a strike price of $120. (Answer the following questions per share).
   1. What is the maximum profit or loss for this strategy?
   2. Draw the payoff diagram for this strategy as a function of the stock price at expiration.
   3. Draw the profit and loss diagram for this strategy as a function of the stock price at expiration.
   4. What is the profit (loss) per contract of this strategy if the share price goes down to $100?
3. Suppose that you had purchased the $150 PUT option at $29.25 per share on March 12, 2021 after you had purchased 100 shares of Apple Inc. one month earlier for $120 per share.
   1. Why would you purchase this PUT? What happens if Apple Inc.s share is trading at $150 per share on April 16 and has fallen below 150?
   2. Why would you be happy with what you had done?
   3. On the same diagram, draw a graph to show the pattern of profits per share from the long stock position, the long PUT option, and the net position (i.e., protective put).

2. [30 points] It is March 12. Apple Inc.s (AAPL) stock is currently trading at US$121.03 per share and has a volatility of 40%. The current risk-free rate of interest is 5% per annum. When solving the following problems, show each step.

1. What is the price of a European CALL option written on this stock with a $150 strike price that expires in 35 days? Price the option using the Black-Scholes model.?
2. What is the price of a European PUT option written on this stock with a $150 strike price that expires in 35 days? Price the option with the Black-Scholes model.
3. Based on your answers to (a) and (b), verify the put-call parity holds.
4. What is the price of a European CALL option written on this stock with a $150 strike price that expires in 35 days? Price the option with a two-step binomial tree model. Would your answer change if it were an American CALL option? Show your work.
5. What is the price of a European PUT option written on this stock with a $150 strike price that expires in 4 weeks? Price the PUT option with a two-step binomial tree model. Would your answer change if it were an American PUT option? Show your work.
6. Using S_uu, S_ud, f_uu, f_ud, S₀ and f from 4.d., calculate the delta, D of the PUT op

PLEASE ONLY ANSWER QUESTION 2