Suppose that the premium on a European put option, p = $3. The time to maturity, T = 1 year. The strike price is $20. The stock price of the underlying common stock is $12 today. The risk-free interest rate is 8% per annum. The stock does not pay dividends.
Observe that there is an arbitrage opportunity.
Clearly state what the trader would do to make a profit.
Make sure that you demonstrate the relation that must be satisfied to eliminate the arbitrage opportunity
First, we note the following:
- we can buy a put for $3
- we can buy a share of the stock for $12
- we spent $15 in total
- we are guaranteed to sell the share for $20 a year later.
Here is the arbitrage strategy:
- Borrow $15 on money market
- Buy a share of the stock and a put option with that $15.
- A year later, sell the share for $20 (using the put).
- The loan a year later will be 15 X 1.08 = $16.2
- The trader made $3.8.
When and how will the arbitrage opportunity be ...
Finding Arbitrage Opportunity