Kappa

What is kappa (vega)?

Kappa—more commonly called vega—is a risk measure for options that quantifies how an option’s price responds to changes in the implied volatility of its underlying asset. It shows the amount an option’s price is expected to change for a one percentage-point change in implied volatility.

How it works

Implied volatility is the market’s estimate of future price movement for the underlying asset and is a key input to option pricing models.
Kappa/vega measures sensitivity to that estimate: when implied volatility rises, option premiums generally increase; when it falls, premiums generally decrease.
Most plain-vanilla long options have positive kappa: they gain value when implied volatility rises. Short option positions generally have negative kappa.

Measurement and interpretation

Units: change in option price per one percentage-point (1%) change in implied volatility.
Example: if an option has kappa = 0.20, a 1-point increase in implied volatility raises the option price by $0.20 per share (or $20 per standard 100-share contract).
Net kappa: the kappa for a portfolio equals the sum of kappas for each position. Traders use net kappa to assess the portfolio’s overall exposure to volatility changes.
Kappa is typically largest for at-the-money options and decreases for deep in- or out-of-the-money options.

Relationship with time and other Greeks

Time to expiration: kappa tends to increase with more time until expiration and declines as expiry approaches, typically approaching zero at expiration.
Other primary Greeks:
Delta: sensitivity to changes in the underlying asset’s price.
Gamma: rate of change of delta as the underlying price moves.
Theta: sensitivity to the passage of time (time decay).
Kappa complements these Greeks by isolating sensitivity to changes in implied volatility.

Practical uses

Hedging: traders construct vega-neutral (kappa-neutral) positions to reduce portfolio sensitivity to volatility swings.
Strategy selection: anticipating a rise in implied volatility (e.g., before earnings or major events) can justify buying options with positive kappa, while expecting volatility to fall might favor selling options.
Risk management: monitoring net kappa helps manage exposure to volatility-driven price moves across an options book.

Key takeaways

Kappa (vega) measures how an option’s price changes with a 1-point change in implied volatility.
It is usually positive for long options, larger for at-the-money strikes, and greater for options with more time to expiration.
Traders use kappa to hedge volatility risk and to size positions around expected volatility changes.