Question

The price of a non-dividend-paying stock is $29. The strike price of a one-year European call option on the stock is $25. The risk-free rate is 3% (continuous compounding). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

Answer 1

Call Option:

Holder of call option will have right to buy underlying asset at the agreed price ( Strike Price). As he is receiving right, he needs to pay premium to writer of call option. Holder of calloption will exercise the right, when expected future spot price > Strike Price. Then writer of option has obligation to sell at the strike Price. Holder will go for call option if he is bullish.

If the Future SPot Price > Strike Price - In the Money
If the Future SPot Price = Strike Price - At the Money
If the Future SPot Price < Strike Price - Out of the Money

Put Call Parity Theorm:

It shows the long term equilibrium relation between Value of call with certain exercise price, Value of put with same exercise price, excercise price, exercise date and stock price today.

Vc + PV of Strike Price = Vp + Stock price

Vc = Value of call
Vp = Value of Put

Partciculars	Amount
Spot Price	$            29.00
Strike Price	$            25.00
Risk free Rate per anum	3.00%
Time period in Years	1

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

PV of Strike Price:
= Strike Price * e^-rt
= $ 25 * e^-0.03 * 1
= $ 25 * e^-0.03
= $ 25 * 0.9704
= $ 24.26

= Spot Price - PV of Strike Price
= $29 - $ 24.26
= $4.74

If the Value of Call is less than $ 4.74, There will be arbitrage exists.