Vega01 bidu theta (which measures time decay, or how much extrin

What Happens in Vega …

Feb 18, 2010, 2:48 am EDT | By Adam Warner

 

Turn on the business news lately and it’s all “Greek this” and “Greek that.” Well, options are on the leading edge of that trend, because we’ve talked Greek since the invention of options.

When it comes to the factors affecting an option’s price, we define pretty much everything in Greek terms, from delta (the rate of change in an option’s price as it relates to movements in the underlying asset) to gamma (the rate of change of delta as the underlying moves). But let’s talk about the one option Greek that’s actually not a Greek letter: vega.

Understanding Vega

Vega is defined as the “rate of change of the options value with respect to a 1-point change in the volatility.”

It is perhaps both the least understood and most important Greek (well, at least since “Jimmy the Greek” passed on to that great sports book in the sky).

I’m going to use the stock Baidu.com (BIDU) to illustrate how vega works. At the time of this writing, if I run a volatility of 38, I show the BIDU March 490 Calls with a theoretical value of $22.

They have a delta of roughly 50, meaning for every 1-point lift (or decline) in BIDU, we would expect these calls to go up (or decline) 50 cents.

They have a theta (which measures time decay, or how much extrinsic value an option will lose every day until expiration) of .32, meaning that they will lose 32 cents of value every day. Keep in mind we’re talking calendar days here, so time decay also affects your options over the weekend.

And, last but not least, they carry a vega of .61. That means that for every 1-point lift (or decline) in volatility, these calls will gain (or lose) 61 cents in value. So for every call contract you own, a 1-point move in volatility equates to a $61 gain or loss.

How common is a 1-point move in volatility?

Well, the BIDU March 490 Calls have close to 30 days until expiration. Here’s a graph of normalized 30-day volatility over the past six months (yellow line):

And as you can see, BIDU volatility fluctuates very often, and quite swiftly. And this is a period where BIDU volatility stayed within a relatively tight range, with a low of about where we are now in the mid- to upper 30s and a high near 50. A year ago, BIDU 30-day implied volatility was as high as 85.

My point here is that vega can have quite a large impact on the overall profitability of a trade.

My example simply references the vega of one unique option, but the most important thing you need to know is your positional vega. That is, how will a 1-point move in volatility effect your entire BIDU position? And here’s where things get tricky, especially if you own (or short) options in multiple expiration cycles.

All vega is not created equal. If I use the same 38 volatility, a BIDU June 490 Call has a vega of 1.14. And let’s say you own the June-March 490 calendar spread in BIDU.

On the surface, it looks like you have a vega of .53 (that’s the vega of the June option you own minus the vega of the March option you sold).

You’d think then that if BIDU volatility rises 1 point, you would earn $53, but there’s one problem. Volatility does not move in unison across cycles. The closer to expiration, the faster volatility moves. So, depending on specifics, a March option may lift 3 points for every 1-point move in the June option.

Below is a graph of normalized 120-day historical volatility for BIDU options (about June now) over the past half year. As you can see, it fluctuates in a much tighter range than the 30-day options, sometimes not even moving at all when the nearer one moves.

The moral of the story is that it benefits you greatly to understand how vega affects your positions, especially on options relatively far away from expiration, because the effect can prove quite large, and it may strike at any time.