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There are a number of ways to look at this: BSM model vega: $$Vega_{call}=Se^{-q\tau}\phi(d_1)\sqrt{\tau}$$ Now if you buy the arguments and assumptions of the model, that means it must be positive mathematically. No matter the value of $$d_1 = \frac{\log\left(\frac{S}{K}\right) + (r-q+\frac{1}{2}\sigma^2)(T-t)}{\sigma\sqrt{T-t}},$$ the value of $\phi(d_1)\...


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