Question

A two-month European put option on a non-dividend-paying stock is currently selling for $2.00. The stock price is $52, the strike price is $55, and the risk-free interest rate is 5% per annum. What opportunities are there for an arbitrageur?

Answer 1

Arbitrage Strategy

Arbitrage opportunity is an opportunity to earn profit without making any huge investment and taking risk. In above case, arbitrageur has an opportunity to earn profit with following strategy :

Today Transaction :

1. Borrow $54 at risk free rate 5% for 2 months
2. Buy Stock at current price i.e $52 with borrowed money
3. Buy Put option at $2.00 with borrowed money

Transaction on maturity :

If Stock Price is more than Exercise Price on maturity :

1. Do not exercise put and sale the stock in open market
2. pay the borrowed money with interest i.e 54*(1+0.05/12)^2 = $54.4509
3. keep rest money as arbitrage profit. i.e (Sale price - $54.4509)

If Stock Price is Less than Exercise Price on maturity :

1. Exercise the Put and sale the stock at strike price i.e $54
2. Pay the borrowed money with interest rate i.e $54.4509
3. Remaining balance is arbitrage profit i.e $55 - $54.4509 = $ 0.5491