Question

The Black-Scholes model shows that the value of a put option increases the longer the time to expiration. Currently, the price of a stock is $100. There are two put options To sell the stock at $100. The tree-month option sells for $7 and the six month option sells for $4.50.

How much do you gain or lose after three months at the following prices of the underlying stock: $85, $90, $95, $100, $105, $110?

Answer 1

Current underlying price of the stock, S = $ 100

Strike Price, K = $ 100

Price of 3-month put option = $ 7

Price of 6-month put option = $ 4.5

After 3 months:

When the price of the underlying stock becomes $ 85:

3-month put option will be exercised : Gain = 100 - 85 - 7 = $ 8

6-month put option will be exercised : Gain = 100 - 85 - 4.5 = $ 10.5

When the price of the underlying stock becomes $ 90:

3-month put option will be exercised : Gain = 100 - 90 - 7 = $ 3

6-month put option will be exercised : Gain = 100 - 90 - 4.5 = $ 5.5

When the price of the underlying stock becomes $ 95:

3-month put option will be exercised : Loss = 100 - 95 - 7 = - $ 2

6-month put option will be exercised : Gain = 100 - 95 - 4.5 = $ 0.5

When the price of the underlying stock becomes $ 100:

3-month put option will not be exercised : Loss = - $ 7

6-month put option will not be exercised : Loss = - $ 4.5

When the price of the underlying stock becomes $ 105:

3-month put option will not be exercised : Loss = - $ 7

6-month put option will not be exercised : Loss = - $ 4.5

When the price of the underlying stock becomes $ 110:

3-month put option will not be exercised : Loss = - $ 7

6-month put option will not be exercised : Loss = - $ 4.5