Question

Consider the following option portfolio: You write a January 2012 expiration call option on IBM with exercise price $172, and the price of the call option is $8.93. You also write a January expiration IBM put option with exercise price $167, the price of the put option is $10.85.

Instructions: for parts a, b, and c, enter your answer as a decimal rounded to the nearest cent.

a. What will be the profit/loss on this position if IBM is selling at $162 on the option expiration date? $

b. What will be the profit/loss on this position if IBM is selling at $178 on the option expiration date? $

c. At what two stock prices will you just break even on your investment (i.e., zero net profit)?

    For the put, this requires that: $

    For the call this requires that: $

d. What kind of “bet” is this investor making; that is, what must this investor believe about IBM’s stock price in order to justify the position?

• betting that the IBM stock price will go up.

• betting that the IBM stock price will go down.

• betting that the IBM stock price will have low volatility.

• betting that the IBM stock price will have high volatility.

Answer 1

A.

Profit for option writer = Total premium received - Total pay off of option

= $19.78 - ($5+0)

= $14.78

Total premium received = call option premium + put option premium

= $8.93 + $10.85

= $19.78

Pay off on call option = Max (S_T -X), 0 = Max( 162-172),0 = 0

where S_T is stock price

X is exercise price

pay off on put option = Max (X-S_T) = Max(167-162 )= 5

B.   Profit for option writer = Total premium received - Total pay off of option

=$19.78 - $6

= $13.78

Pay off on call option = Max (S_T -X), 0 = Max( 178-172),0 = 6

where S_T is stock price

X is exercise price

pay off on put option = Max (X-S_T) = Max(167-178),0 = 0

C. For Put option Break even will be at stock price 147.22

  Profit for option writer = Total premium received - Total pay off of option

=19.78 - 19.78

= 0

pay off on put option = Max (X-S_T) = Max(167-147.22),0 =19.78

For call option Break even will be at stock price 191.78

Profit for option writer = Total premium received - Total pay off of option

=19.78 - 19.78

= 0

Pay off on call option = Max (S_T -X), 0 = Max( 191.78-172),0 = 19.78

D. Investor betting that the IBM stock price will have low volatility.

Because at higher volatility there will chance that option will exercise. writer of option will have benefit if option does not exercise.