Question

Please show work! Suppose you have a relative working for OIC (Option Industry Council). He knows you are taking derivatives class. He shows you the following from CBOE (Chicago Board Options Exchange) market data during the trading hours of the exchange.

Strike Price $50 $55

Put Premium $7 $6

Is there any arbitrage opportunity for you? [Hint: Think if any no-arbitrage property is violated?

You know that if any no-arbitrage property is violated, it would lead to arbitrage! ]

IF no then why?

IF yes then why?

Please show how to prove it mathematically

Answer 1

A put option gives the buyer the right but not the obligation to sell a security at a predefined price level. For the writer of a put option it becomes an obligation to sell the security at the predefined agreed price level on a certain date.

As we can see in the case given there is a scope of arbitrage.

We can sell the put with strike price $50 and take premium of $ 7. Now from the $7 we received, we can buy a put with a strike price of $55 and pay a premium of $6. Hence, we have a net of $1 in our pocket.

1.Now let us assume price of stock is less than $50. Then both puts will be exercised. We have to buy the stock at $50(as we had written a put) and we can sell the stock at $55 (as we bought a put). Thus we have $5 profit. (Also remember we had $1 from premium net)

2. Now let us assume the price is between $50 and $55. Let's say it is $52. Then the put we had written will expire worthless. We can buy the stock at market price of $52 and sell the stock at $55 ( we bought a put). Here again we have a profit

3. Let's assume that stock price is above $55. Let's say it is $60. In this case both puts expire and will not be exercised. (As we can anyways sell at higher than strike price in the market). In this case we have a $1 profit from net premium.

Thus, we can see in all cases it gives us profit. Even with our no investment we end with up with profitt. Thus, there is an arbitrage opportunity present.