In a beautiful paper, http://math.uchicago.edu/~rl/moment.pdf, Roger Lee (2004) shows that implied variance is bounded above by a function linear in the log-strike k.

Does anybody know how it translate for the pdf $f$ or cdf $F$ of the spot if we suppose that $f(x) \sim_{+\infty} \beta / x^\alpha$

Thank you



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