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