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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

\$2.19
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## Forward Price and Arbitrage Opportunity

A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for \$450 per ounce and sell it for \$449 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year (both interest rates are expressed with annual compounding). For what range of 1-year forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid-offer spread for forward prices.

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