Vega & Rho

Vega & Rho

Vega

Vega (ν) measures sensitivity of the option price to changes in volatility:

$\nu = \frac{\partial V}{\partial \sigma}$

For both European calls and puts (they have the same vega):

$\nu = S \cdot N'(d_1) \cdot \sqrt{T}$

Vega is always positive — higher volatility means higher option prices (more chance of large moves). A vega of 0.375 means the option gains $0.375 for each 1% increase in volatility.

Rho

Rho (ρ) measures sensitivity to changes in the risk-free interest rate:

$\rho_{\text{call}} = \frac{\partial C}{\partial r} = K \cdot T \cdot e^{-rT} \cdot N(d_2)$

Rho for calls is positive — higher interest rates increase call values (the present value of the strike decreases). Rho for puts is negative.

Practical Importance

Vega is typically the most important Greek for options traders after delta, as volatility changes can have large effects on option prices.