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ASSIGNMENT 2

Math 174E – Winter 2024

Hubeyb Gurdogan

Release date: Thursday, January 18, 2024

Exercises for Discussion Sections in Week 2

Exercise 2.1 (Hull, Question 1.35)

On May 21, 2020, the spot ask price of Apple stock is $316.50 and the ask price of a call option with a strike price of $320 and a maturity date of September is $21.70.

A trader is considering two alternatives: (i) buy 100 shares of the stock or (ii) buy 100 Septem-ber call options (= 1 call option contract). For each alternative, what is

(a) the upfront cost,

(b) the total gain if the stock price in September is $400, and

(c) the total loss if the stock price in September is $300.

Assume that the option is not exercised before September and positions are unwound (= closed out) at option maturity.

Exercise 2.2 (Hull, Question 1.38)

In March, a U.S. investor instructs a broker to sell one July put option contract on a stock. The stock price is $42 and the strike price is $40. The option price is $3. Explain what the investor has agreed to. Under what circumstances will the trade prove to be profitable? What are the risks?

Exercise 2.3 (Hull, Question 1.40)

A stock price is $29. A trader buys one call option contract on the stock with a strike price of $30 and sells a call option contract on the stock with a strike price of $32.50. The market prices of the options are $2.75 and $1.50, respectively. The options have the same maturity date. Describe the trader’s position by providing the final payoff function at maturity of the combined position.

Exercise 2.4 (Hull, Question 2.36)

What position is equivalent to a long forward contract to buy an asset at K on a certain date T and a put option to sell it for K on that date.

Hint: Determine the payoff of the combined position (long forward plus long put) and identify how this payoff can be created by a different position.

Exercise 2.5 (Hull, Chapters 12.3 & 12.4, Trading Strategies Involving Options)

Consider a trader who is trading call and put options with maturity T ą 0 on a stock.

(a) Provide and draw the payoff profile at maturity T as a function of the stock price ST at time T of following trading strategies:

(i) Butterfly Spread: This position consists of call options with three different strikes but with the same maturity T ą 0. Specifically, the trader buys two call options with strikes K1 and K2 where K2 ą K1 and sells/writes two calls with strike pK1 ` K2q{2.

(ii) Straddle: The trader has a long position in a call option and a put option for the same stock with the same strike and the same maturity.

(b) Draw the trader’s net profit at maturity T as a function of the price of the underlying stock ST at time T of both trading strategies (i) and (ii). In particular, for implementing the butterfly spread strategy does the trader have to pay money or is she receiving money?

Explain carefully.