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.
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.
More about Kappa (Vega)
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.