# Finding Arbitrage Opportunity

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

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#### Solution Preview

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 ...

#### Solution Summary

Finding Arbitrage Opportunity