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      General smile asymptotics with bounded maturity

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          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.

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          Author and article information

          Journal
          2014-11-06
          2015-07-30
          Article
          1411.1624
          faff1a62-94bd-4d97-8002-9a0019fc8312

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          91G20, 91B25, 60G44
          New introduction, added references, improved results for Merton's model. 33 pages, 1 figure
          q-fin.PR math.PR

          Financial economics,Probability
          Financial economics, Probability

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