= Option vega
{title2=$\nu=\partial C/\partial\sigma$}
= Vega
{synonym}
The vega of an <European option> is the derivative of its price with respect to <spot volatility>, holding its other parameters fixed. A dividend-free <European call option> under the <Black-Scholes formula> has $\nu=S_0\sqrt T\,\phi(d_1)>0$. Differentiation proves this because $S_0\phi(d_1)=Ke^{-rT}\phi(d_2)$ and $\partial_\sigma(d_1-d_2)=\sqrt T$. Positivity proves uniqueness of <Black-Scholes implied volatility> for prices strictly between the limiting call-price bounds.
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