Abstract

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [emphMath. Finance, 19 (2009), pp. 1--12]. We present applications to popular models, including the Carr--Wu finite moment logstable model, Merton's jump diffusion model, and Heston's model.

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