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    Finding Arbitrage Opportunity

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    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