Vega
From WilmottWiki
The vega, sometimes known as zeta or kappa, is a very important but confusing quantity. It is the sensitivity of the option price to volatility.
.
This is a completely different from the other greeks since it is a derivative with respect to a parameter and not a variable. This can be important. It is perfectly acceptable to consider sensitivity to a variable, which does vary, after all. However, it can be dangerous to measure sensitivity to something, such as volatility, which is a parameter and may, for example, have been assumed to be constant. That would be internally inconsistent.
As with gamma hedging, one can vega hedge to reduce sensitivity to the volatility. This is a major step towards eliminating some model risk, since it reduces dependence on a quantity that is not known very accurately.
There is a downside to the measurement of vega. It is only really meaningful for options having single-signed gamma everywhere. For example it makes sense to measure vega for calls and puts but not binary calls and binary puts. The reason for this is that call and put values (and options with single-signed gamma) have values that are monotonic in the volatility: increase the volatility in a call and its value increases everywhere.
Contracts with a gamma that changes sign may have a vega measured at zero because as we increase the volatility the price may rise somewhere and fall somewhere else. Such a contract is very exposed to volatility risk but that risk is not measured by the vega.
Formulae
References
- Taleb, NN 1997 Dynamic Hedging. John Wiley & Sons
- Wilmott, P 2001 Paul Wilmott Introduces Quantitative Finance. John Wiley & Sons
- Wilmott, P 2006 Frequently Asked Questions in Quantitative Finance. John Wiley & Sons
