# Vega

- The Vega of a derivative portfolio is the rate of change of the value of the portfolio with the change in the volatility of the underlying assets. It can be expressed as:
- V= , where Î is the value of the portfolio, and Ïƒ is the volatility in the price of the underlying.

- For European options on a stock that does not pay dividends, Vega can be found by:
- V=S
_{0}âˆšTNâ€™(d1), where S0 is the present stock price, T is the time to expiration expressed in years and Nâ€™(d1) is given by:

â€‹

- V=S
- The Vega of a long position is always positive
- A position in the underlying asset has a zero Vega
- Thus its behavior is similar to gamma
- Vega is maximum for options that are at the money