Question

What is a lower bound for the price of a three–month i) European call and ii) European put option on a non–dividend–paying stock when the stock price is $18, the strike price is $15, and the risk–free interest rate is 6% per annum continuous compounding?

Answer 1

Partciculars	Amount
Spot Price	$            18.00
Strike Price	$            15.00
Risk free Rate per anum	6.00%
Time period in Years	0.25

Theoritical Min Value of Call:
= Spot Price - PV of Strike Price

PV of Strike Price:
= Strike Price * e^-rt
= $ 15 * e^-0.06 * 0.25
= $ 15 * e^-0.015
= $ 15 * 0.9851
= $ 14.78

= Spot Price - PV of Strike Price
= $18 - $ 14.78
= $3.22

Theoritical Min Value of Put:
= PV of strike Price -Stock Price

PV of Strike Price:
= Strike Price * e^-rt
= $ 15 * e^-0.06 * 0.25
= $ 15 * e^-0.015
= $ 15 * 0.9851
= $ 14.78

= PV of Strike Price- Spot Price
= $14.78 - $ 18
= $-3.22

As it is -ve Min Value of Put is 0

Instead of buying put to sell after 3 months at strikeprice of $ 15, we can sell the same at Spot Price $ 18 today.

Hence Put option will have no value.

Pls comment, if any further assistance is required.