American Put Pricing Under a Maximally Skewed Stable Model

# Who has introduced the term 'vega' and why?


# Who has introduced the term 'vega' and why?












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?

## Answer by pteetor (score 17, accepted)

https://quant.stackexchange.com/a/135

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".)

## Answer by StackG (score 8)

https://quant.stackexchange.com/a/43793

Joseph de la Vega wrote Confusion of Confusions in 1688, probably the World's first descriptive text on stock market processes and volatility.

I'm not sure that this is why Vega is thus named, but I like to think it's in his honour.

## Answer by Michael Shutze (score 7)

https://quant.stackexchange.com/a/47222

I was one of the floor traders in bond options in the early 80's. Knowledge of options was growing fast at the time primarily lead by the O'Connor brothers who were grain traders from the CBOT. They were the primary force in founding the CBOE. They also developed a large trading operation there in options. When I first started trading bond options most traders didn't not even have delta sheets to price or hedge positions. Floor traders constantly worked everything into arbitrage positions, conversions, reversals, and box spreads. As things developed it became a cottage industry to sell sheets to floor traders. Delta sheets more or less allowed the trader to "delta" hedge positions in the underlying, bond futures, and not be forced to work everything in an arbitrage. One of the individuals selling delta sheets to traders started putting the other Greeks on the sheet. Delta, Theta, and Vega where added. I asked him one day what the Vega represented. I then asked him why he had chosen the term "Vega"? He said it was a Greek letter starting with V as in volatility. I told him that Vega was not a Greek letter but it was a Roman letter, you moron. The next thing I knew all of his competition was putting the 'Greeks" on their sheets including the Vega. They were using Vega because he used Vega. I had my own sheets from my own system. Inside my trading group we used the term Sigma. It is a Greek letter and best describes the derivative. Sigma meaning to sum up. In my opinion as a professional trader volatility is the ball game it is the sum total of what matters in an option trade. As an aside the trader that coined the term Vega blew up bigger than Dallas in the October 1987 stock market crash. Bonds moved a country mile over night due to Fed intervention. I think he lost 6 mill or something in the neighborhood. Oddly enough he had on 1x2 out of the money call and put spreads size large. I had told him a few weeks earlier these trades would eventually kill him. They had almost got me before I understood how they really worked. At any rate he was a moron but as far as I know he did coin the term Vega in the early 80's at the CBOT.

## Answer by Richard Herron (score 6)

https://quant.stackexchange.com/a/138

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.