A particular call is the option to buy stock at $25. It expires in six months an

Question

A particular call is the option to buy stock at $25. It expires in six months and currently sells for $4 when the price of the stock is $26.

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 is $20? $25? $30? $40?
c) If the price of the stock rises to $40 at the expiration date of the call, what is the percentage increase in the value of the call? Does his 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 $10? $15? $20? $25? $26? $30? $40?
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 $20? $26? $40?

I know what a portion of the answer is and I can let you know if your on right track, please no copy and pasting.

Explanation / Answer

a. Intrinsic value of a call is the difference between the current price of the stock and the strike price (specified in the option contract). Intrinsic value is $1.
Time premium (time value) is the rest of the current option price. That is, $3.

b. In 6 months' time the option expires and its time value is zero. However, the option's total value never falls below zero. So the answers are zero, zero, $14, $15.

c. A rise from $4 to $15 will constitute about 167%. It is not clear what is meant by favorable leverage in this particular example.

d. Having bought the stock at $26 and sold the call at $4 leaves us with $22 cost at day 1. The value of the call in 6 months' time will be zero, zero, zero, $10, $1, $5, $15. So the net profit on the operation is going to be:
1) -22 - 0 + 10 = -12
2) -22 - 0 + 15 = -7
3) -22 - 0 + 20 = -2
4) -22 - 10 + 35 = 3
5) -22 - 1 + 26 = 3
6) -22 - 0 + 25 = 3
7) -22 - 15 + 40 = 3

e. The call's value would be zero, $1, $15. Thus, the naked call seller's profit would be 4, 3, -11.

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