# Chapter 9Vega

Vega (, sometimes kappa is used: ) is the change of the value of an option in relation to the change of the (implied) volatility.

It is the derivative of the value of an option in relation to the volatility of the underlying, mathematically: . Throughout the book the Greek letter ν will be used for denoting the vega. The formula for calculating it is as follows: , where is the probability density function. The vega has a log normal distribution.

As earlier mentioned; put call parity dictates vega to be the same for calls and puts, otherwise arbitrage opportunities may arise. Vega will be positive for owning the options (irrespective of calls or puts) and negative for being short them.

The vega is expressed in dollars per option. So if an option would have a vega of \$0.20, like the 50 strike as shown in Chart 9.1, a 1% increase in volatility would make the option (call or put) 20¢ more expensive. A 1% decrease in volatility would result in a 20¢ lower value for the option. ...

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