You notice that shares of stock in the Patel Corporation are...

You notice that shares of stock in the Patel Corporation are going for $$\$ 50$$ per share. Call options with an exercise price of $$\$ 35$$ per share are selling for $$\$ 10$$. What's wrong here? Describe how you can take advantage of this mispricing if the option expires today.

Key Concepts

Intrinsic Value

Intrinsic value refers to the immediate exercise benefit of an option. For a call option, it is calculated as the difference between the current underlying stock price and the strike price, provided that this difference is positive. In the example, the intrinsic value is $50 - $35 = $15, which indicates that the option should not be worth less than $15 since owning the option gives you the right to buy the stock at $35 immediately when it is worth $50 in the market.

Options Pricing

Options pricing incorporates both intrinsic value and extrinsic value (time premium). However, when an option is deep in-the-money and particularly as expiration approaches, its price should be very close to its intrinsic value. A call option priced significantly lower than its intrinsic value indicates a mispricing of the option relative to the stock's current value, which violates the no-arbitrage principle in an efficient market.

Arbitrage Opportunity

Arbitrage involves taking advantage of price discrepancies in markets to realize a risk-free profit. When an option's market price deviates from its intrinsic value, traders can set up positions that exploit this mispricing. In the given scenario, the call option is underpriced compared to the intrinsic value, creating a potential arbitrage opportunity if the option expires immediately. Exploiting this error would involve actions such as buying the underpriced call option and simultaneously taking an offsetting position in the underlying stock to lock in a profit.

Market Efficiency

Market efficiency is based on the idea that asset prices reflect all available information. When mispricing occurs—such as a call option trading below its intrinsic value—it signals a breakdown in this efficiency. Arbitrageurs can then step in, and as they exploit these discrepancies, their actions help to correct the mispricing and restore proper market valuation.

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