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Derivatives Securities and Markets

Problem Set: Option Payoffs

Question #a

Consider a stock priced at $50.  There are several call and put options available that have time to expiration of six months.  There are no dividends on the stock and the options are European-style.  All transactions consist of one contract or 100 shares (i.e. 100 options).   The risk-free rate is practically zero.

Suppose you long an at-the-money call option contract, and hold it to expiration.  Assume the option costs $1.80.

(i) What is the breakeven stock price at expiration on the transaction?

a. $50.00

b. $51.80

c. $48.20

d. $1.80

e. stock price at expiration doesn't matter

(ii) What is your net profit/loss if the stock price at expiration is $49?

a. -$180

b. +$100

c. -$100

d. +$80

e. -$80

(iii) What is your net profit/loss if the stock price at expiration is $51?

a. -$180

b. +$100

c. -$100

d. +$80

e. -$80

(iv) What is the maximum possible profit to you on the transaction?

a. $180

b. $5000

c. $4820

d. infinity

e. zero

(v)  What is the maximum possible net profit to the other party (option writer/seller)?

a. $180

b. $5000

c. $4820

d. infinity

e. zero

Question #b

Repeat the previous question for short position on the call option

Question #c

Repeat the previous question for long position on the put option

Question #d

Repeat the previous question for short position on the put option

Question #e

Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.

Question #f

What is the difference between writing a put option and buying a call option?

Question #g

A trader has a put option contract to sell 100 shares of a stock for a strike price of $60.  What is the effect on the terms of the contract of:  (i) A 5-for-2 stock split  (ii) A 5% stock dividend being paid (iii) A $2 dividend being declared  (iii) A $2 dividend being paid

Question #h

The current price of a stock is $94, and three-month call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (20 contracts). Both strategies involve an investment of $9,400.

What advice would you give?

How high does the stock price have to rise for the option strategy to be more profitable?