English

Short-term at-the-money asymptotics under stochastic volatility models

Computational Finance 2019-03-25 v3 Probability

Abstract

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.

Keywords

Cite

@article{arxiv.1801.08675,
  title  = {Short-term at-the-money asymptotics under stochastic volatility models},
  author = {Omar El Euch and Masaaki Fukasawa and Jim Gatheral and Mathieu Rosenbaum},
  journal= {arXiv preprint arXiv:1801.08675},
  year   = {2019}
}