# Option Kappa

Kappa (κ or Κ) is sometimes used as alternative name and symbol for option vega (ν) – one of the Greeks which measures sensitivity of option price to changes in volatility.

## Kappa vs. Vega: Which is Correct?

Why are there two different names and symbols for the same option Greek?

Vega is by far more widely used. Its main problem is that it is not a Greek letter – unlike the other main option Greeks delta, gamma, theta, and rho. There is no Greek symbol for vega – the symbol typically used is either the Latin v or the Greek nu, which looks similar: ν.

So why is vega used as an option Greek, and what is the problem with kappa?

It is phonetics: vega starts with v as volatility (like theta starts with t as time, or rho starts with r as interest rate). Unfortunately, there is no V in the Greek alphabet – if there was one, it would most likely be the letter used for this Greek.

## Option Kappa Definition and Interpretation

Mathematically, kappa (vega) is first derivative of option price with respect to volatility. It measures how much an option's price (premium) will change if implied volatility increases by one percentage point and all other factors (such as underlying price, interest rate, or time to expiration) stay the same.

## Example

Let's say an option's price is \$2.50, implied volatility is 20%, and kappa (vega) is 0.15.

If implied volatility rises by one percentage point to 21%, the option's price will increase by approximately 0.15 to \$2.65.

Conversely, if implied volatility declines to 19%, the option's price will decrease to approximately \$2.35.

## Kappa Sensitivity to Volatility

Notice the word approximately. Kappa is only accurate for small changes in volatility, because kappa itself also changes as implied volatility rises or falls. This is measured by a second order Greek vomma – the second derivative of option price with respect to volatility.

For more detailed explanation of option kappa (vega), its calculation and use, and how it behaves under different circumstances (with changing strikes, underlying price, time etc.), see option vega.

By remaining on this website or using its content, you confirm that you have read and agree with the Terms of Use Agreement.

We are not liable for any damages resulting from using this website. Any information may be inaccurate or incomplete. See full Limitation of Liability.

Content may include affiliate links, which means we may earn commission if you buy on the linked website. See full Affiliate and Referral Disclosure.

We use cookies and similar technology to improve user experience and analyze traffic. See full Cookie Policy.