General smile asymptotics with bounded maturity

Francesco Caravenna and Jacopo Corbetta

Papers from arXiv.org

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 [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.

Date: 2014-11, Revised 2016-07
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