Question

A 2-month European put option on a non-dividend paying stock is currently selling for $2. The stock price is $47, the strike price is $50, and the risk-free rate is 6% per year (with continuous compounding) for all maturities. Does this create any arbitrage opportunity? Why? Design a strategy to take advantage of this opportunity and specify the profit you make.

Answer 1

The Question above specifies that European has put option on non dividend paying stock
where,
Stock sell = $2
Stock price =$47
Strike price= $50
Risk Free rate = 6% per Year

Put option means :- When the owner has a right to sell the stock at a specified rate.
Strike price:- At this price put option can be exercised.

If the stock price is less than the Strike price then buyer of the put option will be in advantage situation.
where in European will be in money as his stock price is less than the strike price.

Arbitrage Opportunity means a situation where we used to sell or purchase the stock from difference in price.It's a kind of a trade which we make in difference of prices.
For the European it seems to have the arbitrage opportunity. As the strike price is more than stock price which will make him in money.

The Strategy he must follow is :- Exercise immediately
As put option gives the right to holder to sell stock at strike price. Hence , it will be having non - negative value since there will be no loss in the same.
Since the Risk free rate is 6% per annum which means 0.5% per month which means in case if it increases then it will also have the negative impact on the profit.

Profit = Strike price - Stock price
= $50-$47
= $3
Where , European was selling the same at $2 and if we pick the strike price then it will be at $3.