# Volatility of Option

I hope I'm asking this at the right place.

This pertains to actuarial exam MFE/3F on Financial Economics. If $\sigma$ is "volatility" and $\Omega$ the elasticity of the stock, one formula that is taught in this course is

$$\sigma_{\text{option}} = \sigma_{\text{stock}} \cdot |\Omega|\text{,}$$

where "option" means a call or a put.

Finan (Proposition 31.1, pp. 234-235) proves this statement.

My question is, does this formula make an implicit assumption that the Black-Scholes assumptions have to hold?

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I haven't heard of those terms before, but I can tell you that $\Omega = \dfrac{\Delta S_0}{C}$, where $C$ is the call price, $S_0$ is the initial stock price, and $\Delta = \dfrac{\partial C}{\partial S_0}$, the option Greek. – Clarinetist May 27 '14 at 15:13