Question

Assume that a stock is selling at a price of $100.

The 95 call option on the stock sells for $5 and the 105 put option sells for $8.

What is the intrinsic and time value on the 95 call and $105 put?

If the stock increases to $110, what will be the dollar and percentage return on the call option. What will be the return on the put option?

Assume that the investor writes a call option on the above stock. What will be the investor’s gain or loss if the stock closed at $100?

Assume that the investor writes a put option on the above stock. What will be the gain or loss if the stock sells for $110?

Answer 1

Let,

Current Price of Stock = S

Exercise Price or Strike Price = E

Premium Paid = P

**When S>E, call option is exercised and put option is lapsed and vice-versa

Intrinsic Value is given by the difference between Exercise Price and Premium when the option is exercised

i.e., IV = S-E

Time value is given by the difference between option Premium and Intrinsic Value

i.e., TV = P-IV

1. Here, S = 100

(a) Exercise Price, E = 95 Premium, P =5 (call)

Since, S>E therefore call option is exercised

IV = 5

TV = 0

(b) Exercise Price, E= 105 Premium, P= 8 (put)

Since S>E therefore put option will not be exercised

IV = 0

TV = 8

2. S=110 P= 5(call), 8(put)

E (call) = 95 ; E (put) = 105

therefore call option is exercised and put option is lapsed since S>E

Gain (call) = 15 ; Gain (call)%age = Gain*100/P = 15/5 = 300%

Gain (put) = 0 or 0%

***if S=110 is at maturity

otherwise loss is of premium paid = 8 = 100%

3. If S=100 ; P=5

Option holder makes gain of 5 (i.e., 100-95) so the writer bears loss of 5 but P also = 5

overall gain/loss = 0

4. If S=110 ; P= 8

Option holder will lapse the option (since 110>105)

Gain of writer = P = 8