General smile asymptotics with bounded maturity
Pricing of Securities
2016-07-08 v3 Probability
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.
Cite
@article{arxiv.1411.1624,
title = {General smile asymptotics with bounded maturity},
author = {Francesco Caravenna and Jacopo Corbetta},
journal= {arXiv preprint arXiv:1411.1624},
year = {2016}
}
Comments
35 pages, 2 figures. To appear on SIAM Journal on Financial Mathematics