It sounds like an easy question. It wouldn’t be hard if it were a restaurant menu, but when it comes to options, looks can be deceiving.
So, give it a shot. The table above shows some option quotes with the stock trading at $100, 30 days to expiration, and 20% volatility. Which is the cheapest call option?
Most traders will say, “That’s easy! The $100 call is the cheapest since it only costs $2.28. You don’t need to know anything about options to see that!” Well, the reality is you do need to not know anything about options to think that’s the right answer.
If you see option prices in terms of total dollars, you’ll struggle with strategies. All strategies make use of the intrinsic value, extrinsic value (time value), or both. You must be able to identify these values and understand the role each plays in strategies.
To understand which option is the cheapest, remember that calls represent a right—not an obligation—to buy shares. Call options give you a right—the option—to choose. If the stock price falls below the strike, you’re not required to exercise the call and buy the shares. Because you have the right to walk away, the call represents an insurance policy. If that happens, you’d walk away and not exercise the call. You can’t do that as a stock owner. If you own the shares, you take the loss.
With the call, however, you can make all the upside gains if the stock rises, but you don’t participate in all the losses if it falls. That’s a benefit, and in the financial markets, you must pay for all benefits.
The price of option insurance
What’s the value of the insurance? It depends on how likely it is for you to walk away from the deal. In other words, how likely is it for the call to expire out of the money? The more likely, the more you’re going to pay for the insurance. For instance, look at the $100 call at $2.28 above. It’s an at-the-money call, so there’s a high probability for the stock to close below the $100 strike. What are the chances?
Because the current stock price is $100, it’s a 50-50 shot. A 50% chance is the worst level of uncertainty you can have, so you’ll pay the most for the right to walk away for an at-the-money call. However, that doesn’t mean you’ll pay the most total dollars. It means you’ll pay the most extrinsic value. It’s the price of the insurance policy. When it comes to options, it’s the extrinsic value that represents an option’s insurance value.
You can also see the insurance value in the same-strike $100 put. If you owned the shares instead, you could get the identical downside protection by purchasing the $100 put. For instance, if you own the call and the stock falls below the strike, you won’t exercise, so you’ll keep $100 cash. Instead, if you own the shares plus the put, you’ll exercise and collect $100 cash. Either way, you’ll end up with $100 cash, so the call and put offer identical protection, but they’re going about it in different ways. Whether you choose the protective value of the call or put, you’re getting the same protection, so it’ll cost the same $2.28. The $100 call and $100 put have $2.28 worth of extrinsic value, and that’s why both result in identical risk profiles:
Extrinsic value meets intrinsic value
Now, go back to the quotes and look at the $90 call trading for $10.07. With the stock at $100, there’s $10 of intrinsic value, but again, that has nothing to do with the option. Instead, it’s just cash to make the deal fair. If you wish to buy this call, you’re asking the call seller to allow you to pay $90 for shares currently worth $100—a $10 benefit. If the call wasn’t worth at least this $10 intrinsic value, it would result in free money to you. You could buy the call, immediately exercise it, pay $90 for stock worth $100, sell the stock, and pocket the $10 difference. Since no trader is going to give away free money, all call options must trade for at least their intrinsic value. Again, that intrinsic value has nothing to do with the insurance value—the option value. What’s is the insurance worth?
Just as before, we must consider how likely it is for the call to fall out of the money. Even though the stock’s at $100, there’s a small chance it could fall below $90, so you must pay more than $10, just in case you decide to walk away from the deal. With the stock at $100, there’s a relatively low chance for it to fall below $90 at expiration. In other words, there’s a slim chance you’ll be walking away from the deal. If there’s only a small chance that you’ll leave the call unexercised, the insurance must be cheap too. Because the $90 call has $10 of intrinsic value, it must be the residual 7 cents, or extrinsic value, you’re paying for the insurance policy.
So, the $90 call isn’t an expensive option. It’s just $10 of cash, or intrinsic value, plus a tiny 7-cent insurance policy attached. It’s the 7 cents that represents the option. It’s the extrinsic value that you’re paying just in case the stock price falls below the $90 strike.
Naturally, for any option chain, if you continue moving to lower strike calls, you’ll eventually reach a strike where there’s no chance, at least statistically, for the stock to fall below the strike at expiration. At that point, there’ll be no more insurance value. Why pay for an insurance policy if there’s virtually no chance for the stock to fall below the strike?
Now look at the $85 call trading for $15. It’s $15 in the money, so there must be at least $15 of value in the option. That’s the intrinsic value, or cash. However, there’s no additional value over $15—no extrinsic value—so there’s zero insurance value. If there’s no insurance value, there’s no option value. The $85 call is trading for exactly intrinsic value, so it’s trading at parity, which means there’s no difference between the $85 call and shares of stock. Notice that if you pay $15 for the $85 call and exercise it, your cost basis is $100—exactly the same as the current stock price.
Because the $85 call has no insurance value, the $85 put is worthless too. Of course, in the actual markets, you’re not going to see an option trading for nothing. That’s just the theoretical value according to a pricing model. Still, the reason the model says there’s no value for the put is because there’s statistically no chance for the stock to fall below the strike at expiration.
The option pricing relationship becomes clear: It’s the option’s extrinsic value that represents the option’s value—the right to walk away. Now go back to the quotes. Which call strike has the smallest amount of extrinsic value? It’s the $85 call. It’s the one that appears to be trading for the most money, but it’s the most intrinsic value. It’s just cash. Because there’s no extrinsic value, there’s no option.
The bottom line
You’ve probably heard the saying: calls are puts—and puts are calls. It just depends on how we hedge them. That’s why the two risk graphs above are identical, even though the first is a call and the second is stock plus a put. Anything you can do with a call can be done with a put. Now you have a second way to see which call represents the cheapest option. It’s also the put that’s the cheapest, and that’s also the $85 put.
The key takeaway is to understand that the “option” is represented by the extrinsic value—not the intrinsic value. When you learn to see an option’s true price, you’ll make better decisions for strategies.
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