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4

Peter Jaeckel has written various papers on this. "by implication" and "Let's be rational" are the most recent ones. He also provides code on his website www.jaeckel.org. (Note: the question asked for literature.)


1

This is a result of Ledoit et al Lemma proof in Appendix of http://www.ledoit.net/9-98.pdf


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Look on Google for Asymptotic behavior of Implied Volatility Near Infinity you will find results like : $$I(K) \stackrel{K\to\infty}{=} \sqrt{\frac{2}{T}}\left(\sqrt{\ln \frac{K}{C(K)}}-\sqrt{\ln\frac{1}{C(K)}}\right) +\text{O}_{K\to \infty}\left(\frac{\ln\ln\frac{1}{C(K)}}{\sqrt{\ln\frac{1}{C(K)}}}\right)$$


1

What you are trying to do is fit a volatility surface for a given underlying. Once you have a volatility surface you can price an option for an arbitrary expiration and strike. There are numerous approaches to do this and the linear interpolation methods mentioned in the other examples are okay but be careful in the following situations where there is: a ...


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You could check at the methodology for VIX. The VIX itself yields one number - but you might instead return a set of numbers for your skew analysis.


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You use a form of interpolation(start with linear) between the 30 day to maturity IV and the 90 to get the 60,



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