Understanding Stock Option Valuation and the “Greeks”

In my previous four articles on stock options, I’ve given a basic description of what options are and how they can be used to:

(1) generate monthly income by selling covered calls,

(2) purchase stock at a discount by selling puts,

(3) magnify your returns by purchasing calls, and

(4) super-magnify your returns over small price moves by both purchasing a call and selling a higher-strike call (i.e., creating a spread).

There are many other options strategies I could discuss next, but I feel a need to first give a better understanding of how options are valued and how they behave with changes in the underlying stock price (i.e., the Greeks). Can you trade options successfully without knowing this theoretical stuff?  Maybe, but when things don’t go your way, you won’t understand why and you won’t have a good idea how to adjust your position. Anybody can make a lot of money trading options if they know in advance the future direction — and magnitude — of a stock move. Trouble is, stocks often move differently than you expected them to when you put on a particular options strategy. Only great option traders can make money (or minimize losses) in those inevitable situations when the underlying stock moves differently than expected. And what makes an option trader great is his knowledge of the things I will discuss today.

How Options Are Valued

Option prices are derived from stock prices; they do not independently judge the proper value of a stock. In other words, options are priced with the assumption that the underlying stock price is always fairly valued. An option’s value is based on a combination of strike price, time to expiration, interest rates, dividends, and – most importantly – expected volatility around the fair value stock price.  Most option pricing models assume that the likelihood of a stock moving up by 15% is the same in the short term as the likelihood of a stock moving down by 15%. Long-term calls are always more expensive than long-term puts of similar strikes. The reason is that calls provide investors with the upside of stock without the need to incur the significant cost of buying the stock itself, and the interest expense saved in not buying the stock can be substantial, especially over long periods of time. Conversely, interest rates cause put option valuations to decline because the sales proceeds of shorting stock can bring in income, which is lost when you buy puts for downside exposure instead.

Expected Volatility is the King-Pin of Option Valuation

The more the stock price is expected to move above and below its fair value, the higher the implied volatility (IV) of its options and, consequently, the more expensive its options will be. This makes sense since the larger the expected move in the underlying stock price, the more in-the-money (i.e., intrinsically valuable) an option is expected to become. So, when option traders speak of an option being “expensive” or “cheap” they are referring to the option’s IV, not to the perceived fair value of the underlying stock. 

The formal definition of volatility is one annualized standard deviation (in terms of percentage return) away from the current stock price.  One standard deviation for a normal distribution represents the range of return outcomes that will occur 68% of the time. Consequently, an IV of 20% means that the market expects that roughly two-thirds of the time a $50 stock will be trading somewhere between $40 and $60 over the next year. 

To determine the IV of a stock for a period other than one year, you multiply the annualized IV by the square root of the quotient number of days until expiration divided by the 365 days in a year. So the one-week IV of a stock option with an annualized IV of 20% would be: 20*SQRT(7/365) = 2.8%.

Important to remember: the 68% probability inherent in IV calculations is based on a theoretical model and is an educated guess only. It should not be confused with probabilities based on mathematical certainty (e.g., the 1-in-6 odds of throwing a die and having it come up 3).    

One must distinguish between the historical volatility a stock actually exhibits in the marketplace and its IV.  Option prices are based on future expectations (i.e., the IV), not on the past. Consequently, options on a stock that has recently been incredibly volatile could be relatively inexpensive if traders believe such historical volatility was an anomaly (i.e., CEO dies unexpectedly or the company experiences a temporary earnings decline) that won’t be repeated in the future. Academic studies have shown that index option IV has tended to overestimate future actual volatility, resulting in overpriced options. This explains why selling options in conjunction with long stock or long options has proven very profitable over the years.

To find the IV of any stock option series, you can join www.ivolatility.com as a free member and it will show you how the current IV relates to the 52-week range of IV values. You an also go to http://www.optionetics.com/market/rankers/ and see a list of those stock options closest to their 52-week high and those closest to their 52-week low. An option’s IV typically peaks at the time of earnings announcements and, for drug companies, FDA decisions as well. Volatility is “mean reverting,” or oscillates within a range, so that when it is at the low end of the range it tends to increase, and when it is at the high end of the range it tends to decline.  For example, the volatility index (Chicago Options: ^VIX), which is the 30-day implied volatility of the S&P 500 index options, typically trades within a range between about 10% on the downside and 50%-60% on the upside (although during the great 1987 crash, volatility briefly reached an unheard-of 172.79%). Many option traders overweight going long options when the VIX is “low” and overweight going short options when the VIX is “high.” 

Option Greeks

Stocks are simple, dull creatures (think of a manatee); you can own them forever and they either go up, down, or stay flat. That’s it.

In contrast, options are like peacocks composed of many different colors and layers. There are many sides to options and these are explained by “the Greeks,” which measure an option’s performance characteristics.

Delta

The first greek is delta, which measures how much an option price increases for every $1 increase in the price of the underlying stock. By definition, stocks always have a delta of either -1 (short) or 1 (long) — nothing in between — whereas options have a delta anywhere between -1 and 1 (depending whether you are long or short and using puts or calls). Prior to expiration, near-term options with a strike price equal to the stock price (i.e., at the money) have a delta of 0.50 (+ or -).  At expiration, all in-the-money options have deltas of either 1.0 or -1.0 and all at-the-money and out-of-the-money options have deltas of zero. Long calls/short puts have positive delta and short calls/long puts have negative delta. Importantly, unlike stocks, an option’s delta is not fixed but changes with the stock price, which brings us to the second Greek . . .

Gamma

Gamma measures the rate by which an option’s delta changes. For you calculus fans, gamma is the first derivative of delta and is what makes options such a powerful tool in magnifying returns.  All long options have positive gamma and all short options have negative gamma. Let’s assume that a stock is trading for $50 and we are interested in an at-the-money call option with a strike price of $50. Take a look at the following table:

Gamma is greatest right at-the-money (ATM) and diminishes the further out you go either in-the-money (ITM) or out-of-the-money (OTM).  This makes sense since an option’s greatest increase in value occurs when it is transformed from an intrinsically worthless OTM option to an intrinsically valuable ITM option. But the delta of the call continues to increase the further ITM the option becomes and will eventually equal 1. This “delta acceleration” is the leveraged power of options: while a stock’s value increases dollar for dollar, a call option’s gain per dollar of stock upside accelerates. Even better perhaps, a call option’s losses per dollar of stock decline decelerate. Look at the example above: when the stock increases from $50 to $55, the call option gains $2.50 in value ($5 * 0.50 delta), but when the stock decreases from $50 to $45, the call option only loses $2.00 ($5 * 0.40 delta)! It’s pretty cool that long option holders lose less on the downside than they make on the upside for the same size move in the stock! That’s what I call a good risk/reward ratio.

Theta

Options are limited-life instruments and, consequently, the time value portion of their prices decays as the option moves closer to expiration. After all, time value is zero at expiration!  Theta measures the amount of time value decay an option experiences per day.  All long options have negative theta and all short options have positive theta. Theta and gamma are the two most important Greeks; they are the twin pillars that make options special. Whereas gamma is the secret sauce for option buyers (i.e., super-charged appreciation potential), theta is the magical pixie dust for option sellers (income generation).  Theta, like gamma, is greatest at the money. Time value is greatest ATM; the more time value, the more available to decay.  Time value does not decay at a constant rate, but accelerates exponentially the closer you get to expiration. Click on the following link for a chart on time decay: http://www.trading-plan.com/options_time_decay.html.

The water-fall decline in time value takes off around six weeks prior to expiration, so I don’t recommend buying single options during the last 42 days of their lives. However, selling options during this last six weeks is a great way to take advantage of time decay.

Gamma increases exponentially near expiration also. In fact, gamma and theta move in tandem but benefit from completely opposite types of price movement. They are the yin and yang, the light and dark side of the Force, and good vs. evil, all depending upon whether you are a buyer or a seller. If you are long options, you benefit from gamma if the stock makes a strong move in your direction, but are hurt by theta if the stock stagnates. If you are short options, you benefit from theta if the stock stagnates, but are hurt by gamma if the stock makes a strong move.    

Vega

In reality, vega is not a Greek letter, but it sounds like one and is used to measure the sensitivity of an option’s price to a one percentage point change in implied volatility.  As mentioned previously, expected volatility is the main determinant of an options price — the higher the volatility, the higher the option price.  All long options have positive vega and all short options have negative vega.  Consequently, if you expect – or are insuring against – an unsettled market, you want to be long options and, alternatively, if you expect a period of quietude, you want to be short options. 

According to a recent Goldman Sachs study, option trades based on volatility changes are an “alternative asset class” that has low correlation with stock movement. The great thing about a volatility trade is that you can make money even if you don’t have a clue what direction a stock is going to take. Buying a straddle (the simultaneous purchase of a call and a put) makes sense when implied volatility is very low and you expect an explosive increase. Selling put options is a great strategy after a general market panic because the price of options (i.e., implied volatility) skyrockets. People become afraid and are willing to pay almost any price for put insurance – leaving the contrarian put seller sitting pretty collecting the rewards.

Stay Tuned

Next week I will discuss put-call parity and how it helps you understand the price behavior of options spreads and combinations.

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Elliott Gue, editor of The Energy Strategist investment service, has written a wonderful primer on low-risk options strategies entitled “The ABCs of Options to Hedge Risk.” This special options report and four others are yours free if you sign up for a two-year subscription to The Energy Strategist.  No-risk guarantee: For the first three full months if you’re not completely satisfied simply call us for a 100% refund – no questions asked.