Take the 2-minute tour ×
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

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?

share|improve this question
Can you provide more info about this formula? Is Ω the option gearing (or leverage)? –  Quantopic May 27 at 11:38
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 at 15:13

1 Answer 1

up vote 1 down vote accepted

From the definitions and the proof given in the paper you only need a risk neutral measure and the possibility to hedge.

The assumptions you need to make are the absence of arbitrage opportunities (AOA) and the market completeness.

You also work with a constant volatility. I think the result can be generalized to non-constant volatility. There is still an embeded assumption we often forget: the existence of a volatility. The use of a given model will guarantee the existence of the vol, But no need of a bs model.

share|improve this answer
...which then basically sums up most B-S assumptions ;-) –  Matt Wolf May 28 at 14:56
The calculation are made with bs, but it shoul work with time varying r and sigma, whitout brownian motion. –  lmorin May 28 at 15:37
yes as long as you have deterministic r and sigma, as far as I understood the paper. –  Matt Wolf May 28 at 16:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.