Implied volatility interview question [closed]

If an implied volatility of an out of the money call option goes to infinity,what happens to the delta of the said call option?

closed as off-topic by Ric, Quantopik, olaker♦Jun 15 '15 at 15:01

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• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – Ric, Quantopik, olaker
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• Well, first you should have a look at the black scholes formula and think about the implications of an infinite implied volatility – muffin1974 Jun 15 '15 at 6:22
• This is really basic ... let one parameter go to infinity ... – Ric Jun 15 '15 at 9:27

The Black-Scholes delta: $$\partial_SC=N\left(\dfrac{\ln\left(\frac{S_0}{K}\right) +(r - q + \frac{1}{2}\sigma^2)(T - t)}{\sigma\sqrt{T - t}}\right)$$ As you can see this delta would go to$1$ if $\sigma\to\infty$ (and $t<T$).
• Is there any economic interpretation behind what it means if the implied volatility goes to $\infty$? – muffin1974 Jun 15 '15 at 13:16