Option Pricing - Vega and Rho

VEGA

The vega is the change in price of an option with respect to a change in volatility of the underlying security.

 

               change in the price of option

Vega =    ----------------------------

               change the volatility

                                                                

The option price changes as the volatility changes. The absolute change is most pronounced with at the money options and becomes less of a factor with in or out of the money options. However, out of the money options may exhibit a much greater percentage change in price due to their lower absolute price.

The vega is greater the longer the time to expiration. In essence, a change in volatility will affect the price of a longer-term option much more than an option which is closer to expiration. Options very close to expiration will not appreciably be affected by changes in volatility unless the volatility change is extremely large.

The vega is an important measure to know, especially when doing option spreading and delta neutral trading. The vega, theta, gamma, and delta are all interrelated and affect the price of an option. Any comprehensive option strategy must account for all these factors and how each factor relates to the other.

 

RHO

The rho is the change in the price of an option with respect to a change in interest rates.

 

           change in the price of the option

Rho =  -----------------------------------

           change in interest rates

 

Unless interest rates change drastically, the change in volatility, future price, and time to expiration are usually a much greater determinant on option pricing than a change in interest rates.