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The sensitivity of the option value $V$ to volatility $\sigma$ (a.k.a. vega) is different from the other greeks. It is a derivative with respect to a parameter and not a variable. To quote from Paul Wilmott On Quantitative Finance (Wiley, 2nd edition, p. 127):

It’s not even Greek. Among other things it is an American car, a star (Alpha Lyrae), the real name of Zorro, there are a couple of 16th century Spanish authors called Vega, an Op art painting by Vasarely and a character in the computer game ‘Street Fighter.’ And who could forget Vincent, and his brother?

Question. Does anyone know who has suggested to use the term vega for $\frac{\partial V}{\partial\sigma}$ and why it was named this way?

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I hate to be a stick-in-the-mud, but I'm not sure this question is appropriate here. Ironically, it might be more appropriate at english.stackexchange.com –  barrycarter Feb 3 '11 at 0:43
    
@barrycarter Good point, Barry. I don't know if it's an appropriate question, but it sure was fun digging through my dusty old option pricing books, looking for a clue. –  pteetor Feb 3 '11 at 1:03
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I dug through my even older and dustier collection of books (which I refer to as Google Book Search): google.com/… There appears to be a 1985 reference and several 1986 references, though none are really readable. One of the 1986 references definitely refers to d(price)/d(volatility) as vega. –  barrycarter Feb 3 '11 at 8:32
    
@barrycarter <headslap> Of course! Google Book Search -- I shoulda thoughta that! Thanks for looking into it. –  pteetor Feb 3 '11 at 15:50
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2 Answers

up vote 6 down vote accepted

I dusted off my oldest option theory books and searched the indexes for "vega". The oldest reference I found was in Option Volatility and Pricing Strategies (1st ed.) by Sheldon Natenberg, copyright 1988. When discussing the sensitivity of prices to volatility (p. 132), he says,

[T]here is no single commonly accepted term for this number. It is sometimes referred to as vega, kappa, omega, zeta or sigma prime.

Continuing, he adds (p. 134),

Because several computer services popular among traders use the term vega, we will also use this term to refer to an option's change in theoretical value with respect to a change in volatility.

At the time, a popular option pricing service was the Schwartzatron (yes, that was the name), later purchased by Reuters. I have a dim memory that it used the term "vega". Natenberg may have been referring to that service, maybe some other.

That's the oldest reference I can find. Perhaps someone can find an older one.

(PS - I still don't have a clue why they called it "vega".)

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I have no reference, but it's largely phonetic.

Must variables in econ/finance are Greek versions English letter you'd want to use. $\omega$ for weight, $\rho$ for rate, $\epsilon$ for error, and so.

Vega is partial derivative of price with respect to V olatility. But there's no Greek letter for V. Vega sounds kind of Greek.

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