How To Value Call And Put Options

April 10th, 2014

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This blog post was originally published on the blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.

Merton and Scholes, along with Fischer Black (deceased) changed finance forever when they introduced the famous Black Scholes model. In this article, I explain how the model affects options prices in layman's terms.

In the last two articles in this series, I explained what call and put options are. In this article, I'll explain how investors value them.

Today, most investors use a formula called the Black Scholes equation to value both call and put options. Although not perfect, it's relatively simple (compared to other more sophisticated formulas, anyway) and it's accurate enough. In fact, the formula was so well received by investors that its creators won the Nobel prize for its creation.

In this article, I will explain the 4 main factors that influence the price of options, and those are: intrinsic value, maturity, interest rate, and volatility.

Intrinsic Value

First, let's talk about intrinsic value. Intrinsic value is just the value you get if you exercise the option. For example, if you have a put option with a strike of $50, and if the stock is trading at $30, that means you can buy the stock today and exercise the option to sell the stock for $20 profit. This $20 is the intrinsic value.

Often times, the intrinsic value of an option is 0. For example, if you have a call option with a strike of $40, and if the stock is trading at $30, then it doesn't make sense to exercise the call option today since doing so would lose you money. In this case, the intrinsic value is 0.

Therefore, the value of options increase when intrinsic values increase. This is pretty easy to understand.


Maturity refers to the length of time you have before the option expires. The longer the maturity, the more valuable the option.

Think of it this way. I explained in my previous article that put options are like insurance. The longer the insurnace protects you from bad events, the more valuable it is.

For call options, we can think of it as borrowing money for a longer period of time. Doing so costs us more in terms of interest, and since we're paying for all of that up front, call options cost more.

Interest Rates

Interest rates have opposite effects on the value of call and put options. Taking the analogy of borrowing money again, call options cost less when interest rates are lower.

However, it's not so easy to explain why put options cost more by continuing to use the analogy of insurance. It's not that the analogy breaks down - real insurance costs more in low interest environment as well - but people generally don't understand why.

Here, I'll move away from the analogy and go back to first principles. Put options are a protection against the stock losing its value. Now, let me ask you a question. With all other things equal, which stock has the greater potential to lose its value? The stock with lower return potential, or higher return potential?

The answer: the stock with higher return potential. To see why, let's say that we have stocks ABC and XYZ. Both stocks have a band of 20% around its expected return in a year. ABC has an expected return of 10% per year, while XYZ has an expected return of 20% per year.

In this case, we can expect ABC to return between -10% to 30% in a year, whereas we can expect XYZ to return between 0% and 40% in the same year. If we were to buy put options for both of these companies, XYZ's would cost less than ABC's, because the chance of XYZ's stock going down is smaller.

So what does this have with interest rates? Well, in an efficient market, (I know. Bear with me.) the expected return of any stock is inextricably linked to interest rates. Since stocks are riskier than bonds, and since higher risk should be compensated with higher expected returns, stocks should have greater expected return than bonds.

Therefore, when interest rates rise and bonds have a higher expected rate of return, the expected rate of return of stocks go up as well. This leads to a lesser chance of the stock going below the put option's strike price, which leads to lower price for said put options.

Of course, in the real world, the markets are not that efficient. When a put option implies a greater expected rate of return on a stock than you think it deserves, that might be an opportunity to buy.

However,of the 4 factors I discuss in this article, I find that interest rate has the least effect on option prices in general. Therefore, I don't think people should act on their conviction on expected returns unless their views differ substantially from the market's view.


Lastly, but perhaps most importantly, the value of options depend on its implied volatility.

Simply put, implied volatility refers to how uncertain the markets feel about a stock's future. Implied volatility is typically higher for speculative companies such as junior mining companies with no existing production. On the other hand, implied volatility is lower for stable stocks like utility companies.

The higher the implied volatility, the higher the price of the option. For put options, going back to the analogy of insurance, higher volatility is like having a higher chance of your house burning down. Premiums go up in such cases.

For call options, remember that unlike borrowing money, buying call options mean you can only lose what you put in (i.e. limited liability). For stocks with higher implied volatility, there's a greater chance that you'll take advantage of this limited liability, which means you pay more for obtaining this privilege.

When you disagree with the market's view of a stock's volatility, that might also be an opportunity for you to buy options. If you think a company's future is more uncertain than what the markets give credit for, the option may be undervalued. In fact, this is the primary reason I buy options.

Case Study: BMO

Just to give you an example, a couple of months ago, I bought put options on Bank of Montreal stock. The reasons are two-fold.

First, I think there's a good chance that banks' profits will go down.

Banks make their money by lending to consumers and businesses. But the Canadian consumers in particular are up to their eyeballs with debt. When the opportunity to lend to credit worthy borrowers diminish, bank profits go down as well.

But second and more importantly, the implied volatility on their options is low.

Over the past 100 years, the TSX index as a whole had an average volatility of about 15~20%, depending on how you calculate it. But when I bought put options on BMO, the options had an implied volatility of about 18%. In other words, a single stock within the TSX had the same volatility as the whole TSX historically.

I know Canadian banks are generally safe, but is it THAT safe? I can easily think of scenarios where the bank's stock could crash. For instance, if the housing market crashes, you can be sure that bank stocks will follow. For banks, there's also a possibility that losses will come from the left field, like it did with SocGen.

So why are BMO's put options cheap? Here's my guess: ZWB. Anytime someone invests in ZWB, the money goes towards selling call options, which ends up driving down the implied volatility. I'll discuss this ETF in detail in a later article.

In summary, option prices are influenced by 4 major factors: Intrinsic value, maturity, interest rates and implied volatility. When you disagree with the market's view on a stock's expected return or its implied volatility, that creates an opportunity to trade options.

This blog post was originally published on the blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.

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