Implications of unlimited potential

Quantitative Finance Level 1

True or False?

Assume that the price of a stock is $100.
Consider a call option (of any strike) on the stock. Because the call option has unlimited profit potential, hence there is no upper bound on the price of the call.

False True

1 solution

Chew-Seong Cheong
Mar 19, 2015

A call option gives a right to the option holder to purchase one share stock for a certain price. The option itself cannot be worth more than the stock, if not we can make profit by selling an option and buying a stock. Therefore, the upper bound on the price of a call is the share price.

For more see Upper and Lower Bounds of Options .

If the underlying stock price can go to infinity, then the call price could go to infinity minus the strike price, that is not bounded. Either way, this is a very stupid question.

Patrick Nehls - 5 years ago

100 shares

Craig Brownell - 5 years, 3 months ago

It usually represents 100 shares, if the underlying is a publically traded stock on the US exchange. However, there are mini options for 10 shares, and jumbo options for 1000 shares too.

Furthermore, options issues privately (e.g. companies to employees) often correspond to just 1 share.

Calvin Lin Staff - 5 years, 3 months ago

I think this is a tricky question. Of course it has a limit of (stock price - strike price), but we are assuming that this difference is going to infinity.

Illan Lois - 2 years, 11 months ago

Part of the misconception is that people forget one way of determining option prices is through the cost of hedging the outcome. In this case, the stock price is a natural upper limit, because if you can sell the option for $S_i + \epsilon$ , then what you would do is to buy the stock and let the trade settle. If the stock settles above the strike price, the option is exercised and you loss the call and make $\epsilon$ . If the stock settles below the strike price, the option is not exercises and you can sell the stock to make $S_f + \epsilon$ .

Note: I'm avoiding issues like transaction costs, interest rates, etc.

Calvin Lin Staff - 2 years, 11 months ago

Agreed, should stipulate is there a limit to the price of the call while stock price trading at 100 if this the question. Ambiguous the way it is worded otherwise.

Steve D - 1 year, 3 months ago

That is what the first sentence is stating. Let me know if you have a much better suggested phrasing.

Note: I want to avoid a scenario where something thinks "the stock price can only trade at 100 for the entire lifetime of the call option".

Calvin Lin Staff - 1 year, 3 months ago

Agreed - question is not properly formulated

Guillaume De Lamaziere - 1 year, 1 month ago

Question poorly formulated

Bruno De Pau - 2 months, 1 week ago

Implications of unlimited potential

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