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Understanding the “Greeks,” Part 3: Vega

Understanding the “Greeks,” Part 3: Vega
March 07
00:23 2012

The analysis of options includes four important risk metrics, which are identified by the Greek letters delta, gamma, vega, and theta. (Based on that, it should not be difficult to imagine why these four metrics are collectively nicknamed the “Greeks.”) Here we’ll examine what the third Greek, vega, measures. (This discussion will require an understanding of the fundamental workings of options, so if you do not have a good grasp of those concepts, please first review some of our material on options basics.)

It is important to recognize that all of the Greeks are derived from mathematical models. They are not “hard” numbers like an option’s price, bid/ask spread, volume, or open interest. For that reason, the Greek measures are only as good as the model that underlies them—something you should carefully consider before relying heavily on a particular set of Greeks to develop a trading strategy. This is also why you will see different conventions for representing the value of any given Greek.

Vega is related to volatility, but don’t make the mistake of assuming that this is what vega measures—there are other metrics for volatility—or that the relationship is direct. Instead, vega measures the sensitivity of the option to changes in the volatility associated with the underlying stock. Specifically, it represents the dollar change in the price of an option that will result from a 1% change in the volatility level of the underlying security. For this reason, its value may be positive or negative, depending on the effect the volatility change would have on the option in question.

An increase in volatility will cause an increase in option contract pricing, and this holds true for both calls and puts. The reason is simple: an option writer is betting on the direction of a given stock’s price within a limited timeframe, and higher volatility makes the task of predicting the likelihood that a stock will or will not achieve a certain strike price more difficult. More difficulty in making predictions means more risk, so a risk premium gets tacked onto the option price.

For the same reason, at-the-money options are affected more than in-the-money or out-of-the-money options. As we discussed in the explanation of gamma in Part 2 of this series, a small change that pushes the stock price above or below the strike price is much more likely than the much larger change needed to move an in-the-money option out of the money, or vice versa. Volatility only increases this likelihood, and to a much greater degree for small changes.

Finally, calls are thought to be impacted more strongly than puts. We must confess that there are no hard-and-fast explanations of why this is the case—and not even perfect certainty that it is the case, frankly—though there are certainly theories.

Volatility is to a great extent a function of market psychology, and the implied volatility that vega measures reflects what the market expects. For that reason, vega can change even when the price of the underlying issue has not moved, and should events occur that the market feels are likely to produce substantial price changes (whether up or down) in that stock, vega will increase.

Since it is tied directly to the degree of risk associated with the option contract, vega falls as expiration approaches. As we have seen with delta and gamma, the less time that remains on an option contract, the smaller the chance of substantial changes in the price of the underlying stock.

In closing, we’ll return to our examples of Amazon (AMZN) and Bank of America (BAC) to see vega in action. As in Parts 1 and 2, this data is as of February 20 for March contracts, with AMZN at $182.50 and BAC at $8.02.

AMZN BAC
Strike Price Vega Strike Price Vega
155.00 0.00 4.50 0.00
160.00 0.07 5.00 0.00
165.00 0.10 5.50 0.00
170.00 0.14 6.00 0.00
175.00 0.17 7.00 0.00
180.00 0.19 8.00 0.01
185.00 0.19 9.00 0.01
190.00 0.18 10.00 0.00
195.00 0.15 11.00 0.00
200.00 0.11 12.00 0.00

At first glance, you might find these numbers a bit startling. Amazon is a large, highly successful online retailer with a share price approaching $200, whereas Bank of America is as beaten up as any large bank stock in the wake of the 2008 financial crisis and the potential troubles that linger in Europe, with a share price under $10 that had dipped to near $3.00 in early 2009. Why, then, is its vega almost nonexistent across such a wide range of strike prices while Amazon’s is so much higher by comparison? (Even Amazon’s vega numbers are low in the grand scheme of things, we should note.)

Remember that vega measures option price sensitivity to changes in implied volatility. Suffice it to say that option writers for BAC contracts have already built a fairly substantial risk premium into their options, given the nature of the stock, so there isn’t much out there that could unsettle them.

Where AMZN is concerned, however, the stock is considered to be stable and relatively “safe” and predictable. Were volatility to suddenly increase sharply, that would be a sign of serious potential problems for AMZN, so it would warrant a much more substantial adjustment to the option price. Notice too, however, that vega drops to zero for the $155 strike price, so apparently the market does not feel that even very bad news would be likely to pummel the stock all the way to $155 before contract expiration.

As with delta and gamma, there are option strategies that can be built around vega analysis. In its simplest form, however, this metric is a good indicator of what the market expects from a given stock in terms of volatility.

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