Valuing Options

The value of an option is determined using option valuation models. These models can figure out the current value using certain inputs and can also calculate the hypothetical value based on changes of the different inputs into the model. The most popular model is based on a formula called the Black-Scholes Formula.

The Black-Scholes formula

The Black-Scholes model was the first formula that was able to accurately determine the value of an option. The formula was created by Fischer Black and Myron Scholes and was one of the biggest breakthroughs in the history of theoretical finance. Their ground-breaking work led to a Nobel Prize in Economics in 1997 for Myron Scholes and Robert Merton, who was the first to publish a paper about Black-Scholes (Fischer Black was ineligible for the prize because of his death in 1995).

Beyond Black-Scholes

Over the past 20 years or so there have been theoretical advancements made to options valuation due to new insights about the impact of volatility and other factors. But for a beginner it is fine to use the Black-Scholes formula as your valuation tool.

Factors

Although the math behind the formula is very complex, it is not hard to conceptually understand what determines the price of the option. The variables that are put into the Black-Scholes formula are as follows:

The price of the underlying security. The market price of the underlying security. A rise in price will increase call price and decrease put prices and vice versa.
Strike price. The price at which the option can be excercised. Also, the price at which the option begins to accumulate intrinsic value.
Time left until expiration. The more time until expiration the more the option will be worth. Time value decay accelerates as expiration gets closer.
Implied Volatility. This is the estimation of the volatility of the underlying security during the life of the option. Everything else being equal a higher level of volatility will mean a higher option price. This is because the higher the volatility the higher the probability a security will hit a certain price.
Interest rate. The risk-free interest rate until the option expires. A rise in interest rates results in higher call option prices and lower put options prices and vice versa.
Dividends. The higher the dividends are the lower the call premiums and higher the put premiums will be.

About implied volatility

Volatility is the most important input into the options model. This is because it is the only input that is a user-defined variable (unlike interest rates and dividend rates for example). So implied volatility, by default, becomes the only input that changes due to supply and demand. Because of this, implied volatility then becomes the valuation metric of the option.

You can think of implied volatility as the "P/E ratio of options". When tons of people buy an option the price of that option then goes up. Since all of the other option variables are "fixed", the implied volatility goes up as the price of the option goes up and vice versa. So when the implied volatility goes up too much it means you are paying too much for the option.

If you get seriously involved in options you'll find that advanced options traders even quote option prices in terms of volatility (i.e. "The Intel January 55 calls are trading at 24 percent.").

So now that we know that implied volatility is the valuation metric of the option, the next question becomes: "How do we know if the implied volatility is too high or too low?" Well, like any valuation metric there are no objective rules to tell you exactly what the value should be but there are indicators that you can use as guidelines.

The first indicator you can use is the historical volatility of the underlying security. We calculate the historical volatility by looking at the volatility of the underlying security over the last x days (called the "lookback period"). How many days back should you go? Again, this is subjective. Some say you should use the number of days that the options had left until expiration so that the time frames will be the same. Others say you should use the last 30 days because the most recent activity will the best indicator of the future volatility.

So if the historical volatility of Intel stock is 15% and the Intel options are trading at 25% volatility then the options may be overvalued. The fact that the options' volatility is higher than the stock's volatility should be a red flag. When this happens the options market is saying that the volatility of Intel stock will be higher in the future (the future being the life of the option) than in the past. The problem with this scenario is that the options' market prediction may turn out to be a correct one - the volatility of Intel stock in the future may indeed rise. So this indicator needs subjective analysis to be useful.

Another indicator you can use is the historical volatility now compared to what the historical volatility has been in the past. This method is based on the premise that there is generally a "normal" level of volatility that a stock will have over time. Therefore, the stock's volatility has an average it tends to trade at and the volatility will tend to be "mean reverting", which means that if volatility becomes too high or too low that it will tend to go back to the average.

For example, if a stock comes out with really bad earnings and the stock drops 50% in one day, the historical volatility of the stock will therefore rise dramatically due to this huge price change. Consequently, the implied volatility of the options will also shoot up because the underlying stock's volatility has. But is historical volatility an accurate gauge of future volatility in this case? In other words, will the underlying stock's volatility stay at this new higher level? Definitely not. Stocks certainly can fall 50% in one day but drops like this will happen in a particular stock only once every few years, if ever. Therefore, it is obvious that the volatility of the stock will go back down as the stock calms down. In this case you can use the past historical volatility of the stock as an accurate guide of where implied volatility will be heading. In this case the implied volatility will tend to go back down so you will not want to engage in any long-premium strategies because you will be buying at the top of the volatility spike. This is one of the biggest mistakes amateur options traders make. They notice a stock that has moved by a huge amount and form the hypothesis that the stock is more likely to make a big move now than in the past. Although this is a correct assumption, they ignore the fact that the option has already baked in this higher likelihood of big price movement by pushing the implied volatility up. More accurately, the option has "overbaked" the likelihood of a big price change because of underlying volatility is at an temporarily high level.

In a case like the one illustrated above you can see how volatility really is the valuation of the option. As implied volatility rises you are paying more for the exact same option. In other words, the lower the implied volatility, the cheaper the premium is. So when you buy an option you want to have an opinion about what the underlying security will do but it is wise to have an opinion about whether the you are paying too for the option. You can think of an option trade as making two different trades at once. The first is betting on the direction of the stock and the second one is betting on the directon of implied volatility. If the implied volatility for an option rises then - everything else being equal - you will make money. If the implied volatility for an option falls then - everything else being equal - you will lose money. The reason most traders don't realize this is because there are so many other variables that are simultaneously affecting the option price (mainly the price of the underlying security) that they don't bother to isolate the volatility factor. Other traders simply don't care. They write off the level of implied volatility of an option as being inconsequential. But it isn't. Volatility is such an important component of the value of an option that some people refer to trading options as "trading volatility".

Another indicator you can use to estimate the correct level of implied volatility of an option is the implied volatility of other options of the same security. This is an example of using "relative valuation" where we are comparing the valuation of of simialr secuties to each other. The danger here is that if all the options for a particular stock are overvalued then this metric won't alert us to that fact.

My opinion

As a beginning trader don't waste your time with the math involved with options. Get to know the variables and how they affect an options price. If you have a PhD in math and want to get deep into the calculus of the valuation formulas then go for it. But if you do this keep in mind two things. First, there are very little arbitrage opportunities - especially for retail traders - so don't get hooked on the idea that you'll be able to squeeze out easy profits by finding mis-priced options.

The second thing to remember is that getting tied up in theory has it's own downside. By worrying about the technical minutia of how markets work you miss out on learning the critical success factors in trading like learning about market psychology. This is particularly applicable to anyone who has a PhD or someone coming from the hard sciences like physics. These people tend to view the market as a mathmatical formula that has a static solution instead of the dynamic animal that it is.

Education > Investing > Options > Options Valuation

Valuing Options

The Black-Scholes formula

Beyond Black-Scholes

Factors

About implied volatility

My opinion

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