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Pardon Me, but Did You Say Your Name Was Vega or Tau?

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People refer to one of the Greeks of option pricing as vega, but it turns out there's no "vega" in the Greek alphabet. The alphabet does include a "tau," so some options traders prefer the name "vega," and some, "tau." They mean the same thing.

This article will employ the word "vega" because it's the term bandied about most often. By whatever name it's called, vega details how much an option's price changes when volatility moves by one percent. For example, on November 30, Google (GOOG) closed at $693.00. At that time, GOOG's DEC 700 put featured a vega of 0.66. For each one percent rise in volatility, vega would theoretically contribute an extra $0.66 gain to the option's value. For each one percent drop in volatility, vega would theoretically subtract $0.66 from the option's value.

Okay, that's easy enough to understand, but which volatility is causing vega to add or subtract from the option's value? Discussions about volatility can get all wonky. Some people assume their options' price is based on the VIX or VXN, depending on whether they're trading NYSE or NASDAQ-listed stocks, but is that true? Maybe we're talking about the volatility of the underlying: the stock, index or other security being traded. Or is it the volatility of the option itself that goes into the pricing? And if it's the option's volatility being measured, is it the historical or implied volatility?

See why I saved the discussion of vega for last in the series of articles on the Greeks?

Lawrence G. McMillan, writing in OPTIONS AS A STRATEGIC INVESTMENT, says "vega measures how much the option price changes as implied volatility [of an option] changes" [860]. McMillan points out that options' traders, hearing of some potential development in a company, may drive up the implied volatility and, therefore, the price of the options on that company, but the historical volatility remains the same as it was before the development surfaced.

Traders who are relying on the VIX or VXN as a guide to whether a particular option's implied volatility will climb or deflate are sometimes confounded. Perhaps the VXN is falling, for example, while rumors start circulating that a four-lettered biopharm company is about to receive word from the FDA on one of their drug trials. Implied volatility on that company's options may skyrocket while the VXN is dropping.

Sometimes there's a general correspondence in VIX or VXN action and the implied volatilities of many stocks--implied volatilities of many will tend to rise when markets are particularly volatile and the VIX and VXN are also rising, for example--but you can't depend on that correspondence if you're trading options on individual stocks.

Okay, that's settled, or settled according to the word of Larry McMillan. But why do you need to know about vega? If you're an option buyer, you generally want to buy when options are cheap, and that's when their implied volatilities are low compared to historical volatilities. Your hope is that implied volatility will revert to the mean or norm, climbing toward the historical value. As that happens, your positive vega will contribute to an escalation in your option's price. The larger the vega, the more the contribution.

If you're an option seller, you generally want to sell when implied volatilities are high compared to historical volatilities. You're hoping for a reversion to the norm, too, with implied volatilities sinking toward historical levels. As volatility changes, vega will tell you how much the option's price will deflate. The larger the vega, the larger the deflation.

Those are generalizations, of course, and generalizations never hold in all circumstances, but it's a good sort of beginner's guide. For example, understand that during amateur hour, the first hour of trading each market day, options' prices are often inflated, plumped up by extra volatility, and they often revert to the mean after that first hour. That means that some of the value that's tied to volatility will be leaking out of them, perhaps even as the underlying moves in the right direction for your play. If you've bought 4 SPX ATM calls first thing on a Monday morning, for example, you need the SPX to move up quickly or you'll soon be finding your position underwater when that initial volatility dies down. Vega will give you an idea how much your option's value will deflate as the volatility dies down.

Of course, I don't foresee many of you checking out vega when you're scrambling to get into a long call or put play early in the morning. Also, of course, you can make money buying high and selling higher going long options or selling low and buying-back lower when selling options, but understanding how vega works helps you to at least make considered decisions.

SSo, how does vega work? It's always positive when you buy options, whether they're puts or calls. That means that the price of the underlying can just sit there, but if the volatility escalates, vega will theoretically add to the value of both puts and calls. Of course, other factors are showing up in the option's pricing, too, and time decay is going to start working against an options' value if the underlying just sits there for a long-enough period, whether or not volatility is escalating or declining.

Vega is always negative when you sell options, whether they're puts or calls. It's always zero for a stock position because it doesn't matter what the volatility of that stock is, its price is its price. You don't pay $4000.00 for 100 shares of a $40.00 stock when its volatility is low and $6000.00 for 100 shares of a $40.00 stock when its volatility is high. When it's $40.00, you pay $4000 for those 100 shares.

If you're long options, you're long vega, and you benefit from an increase in implied volatility. The increase plumps up the price of your options. They're worth more. When you're short options, you're short vega, and your position is hurt when implied volatility increases. That's why vega is negative for options you sell or write options. The relationship is an inverse one.

You can calculate position vega for your total positions, too, and not just for individual options. For example, imagine that on December 6, you had entered a Jan 1530/1540 bear call spread--probably not a good idea, but this is an example. The Jan 1530 call had a vega of 1.19; the 1540, a vega of 1.09. Imagine that you set up that position by selling 10 contracts of 1530 calls and hedged by buying 10 contracts of the 1540. What's your position vega? Will you be hurt or helped by an increase in volatility?

Your position vega was as follows:
1530 calls: 10 contracts x 100 multiplier/contract x -1.19 vega = -1190 vega.
1540 calls: 10 contracts x 100 multiplier/contract x 1.09 vega = 1090 vega.
Position vega = -1190 vega + 1090 vega = -100 vega

Your position vega is negative. That means that you will suffer a loss for each percentage that IV increases, a $100 loss. If your position vega is negative, you want volatility to decrease, not increase. A credit spread will always be negative vega. That's why credit spreads are hurt in two ways: by an increase in volatility and an adverse price move.

As you probably suspect already from what we've learned from our study of the other Greeks, vega is greatest for ATM options. It's zero or nearly zero for deep-in-the-money options or far out-of-the-money ones. If an option is deep ITM, its price is going to move pretty much in lockstep with the price of the underlying, and that's not going to be impacted by a change in implied volatility of the option. If an option is far OTM, it's not going to move much with the price of the underlying and a change in implied volatility isn't going to impact it much.

Vega is always higher for options with more time remaining until expiration. To some degree, the particular strike that has the highest vega is impacted by the time remaining before that option expires. If you go further out in time than three months, McMillan claims, an option that's slightly out of the money may have a higher vega than the ATM one.

To test that statement, I hunted around until I found a stock that closed November 30, when I was first fleshing out this article, at the money or nearly at the money for one of the strikes of its options. ONEOK Partners LP (OKS) was one, closing at $60.03. The ATM JUL 08 60.00 calls featured a vega of 0.18 while the slightly OTM JUL 08 55.00 calls exhibited a vega of 0.15, and the also slightly OTM JUL 08 65.00 sported a vega of 0.16.

Hmm. That didn't turn out as McMillan predicted it would. The ATM had the highest vega just as it would for a near-term option. Were these options too far out? A quick check of the APR 08 expiration calls turned up a similar result. Would the result be different if puts were used instead of calls? Nope. The ATM's were still the most expense.

The SPX JUN options exhibited the effect McMillan noted. With the SPX at 1481.14 in early December, the almost at-the-money 1480 calls and puts had vegas of 4.24 and 4.26, respectively. The 1485 calls and puts had vegas of 4.26 and 4.28, respectively, each slightly higher than the more nearly ATM options. Vegas for the 1475 calls and puts were both smaller than for the more nearly ATM options.

A quick and far-from-systematic or exhaustive scan does not confirm McMillan's report that for options with more than three months to expiration, the slightly OTM options will have vegas higher than the ATM ones, but even McMillan reports that this effect disappears as expiration approaches. I'm not sure that one should factor in this supposed oddball effect into strategy planning, as my quick search could not confirm the effect.

A similar oddball effect with regard to slightly OTM and ATM options supposedly exists for options on stocks with the highest volatilities. McMillan claims that slightly OTM options will also sport vegas slightly higher than ATM options on these stocks.

That may be more than you want or need to know about vega. Those peculiarities may not be something that concerns you, particularly since they could not be confirmed to exist. What you do need to know is that you're long vega when you're long options, and that means that you benefit from an expansion in volatility. You're short vega if you've sold or written options, and you're hurt by an expansion of volatility. The volatility that concerns you is the implied volatility of your options. If you're trading options on individual stocks, you can't rely on VIX or VXN to adequately alert you to any changes in implied volatility of the options you're trading.

That's about it. We may return to some ideas about the Greeks of options, perhaps following a trade through its initiation and then conclusion, seeing how the Greeks might help with the initiation or conclusion of the trade, but we'll have to see what develops. I think it will soon be time to look again at the corrective fan theory now that markets have been zooming this week, and we can also look forward soon to a guest article on standard deviation and how it relates to trading.

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