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), 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.
Caravenna, F., Corbetta, J. (2016). General smile asymptotics with bounded maturity. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 7(1), 720-759 [10.1137/15M1031102].
General smile asymptotics with bounded maturity
CARAVENNA, FRANCESCOPrimo
;CORBETTA, JACOPOUltimo
2016
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), 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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