Question

A particular call is the option to buy stock at $35. It expires in six months and currently sells for $6 when the price of the stock is $36.

a) What is the intrinsic value of the call? What is the time premium paid for the call?

b) What will the value of this call be after six months if the price of the stock is $29, $35, $39, and $50, respectively?

c) If the price of the stock rises to $50 at the expiration date of the call, what is the percentage increase in the value of the call? Does this example illustrate favorable leverage?

d) If an individual buys the stock and sells this call, what is the cash outflow (i.e., net cost) and what will the profit on the position be after six months if the price of the stock is $19, $22, $29, $35, $36, $39, and $50, respectively?

e) If an individual sells this call naked, what will the profit or loss be on the position after six months if the price of the stock is $29, $36, and $50, respectively?

PLEASE SHOW WORK

Answer 1

a]

The call is in-the-money as the strike price is lower than the stock price.

Intrinsic value = stock price - strike price = $36 - $35 = $1

Time premium = option premium - intrinsic value

Time premium = $6 - $1 = $5

b]

If the stock price at expiration is lower than the option strike price, value of call option = $0

If the stock price at expiration is higher than the option strike price, value of call option = stock price - strike price

c]

The option value has increased from $6 to $15.  

% increase in option value = ($15 - $6) / $6 = 150%

% increase in share price = ($50 - $36) / $36 = 38.89%

Yes, this is a favorable leverage because the % increase in option value is much higher than the % increase in share price

d]

cash outflow = price of stock - premium received = $36 - $6 = $30

Profit on position = profit on stock + profit on call option

profit on stock = ending stock price - purchase price

profit on call option = premium received + ending option value

e]

profit on call option = premium received + ending option value