Asymptotic Smiles for an Affine Jump-Diffusion Model
Abstract
In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work.
Keywords
Cite
@article{arxiv.2003.00334,
title = {Asymptotic Smiles for an Affine Jump-Diffusion Model},
author = {Nian Yao and Zhiqiu Li and Zhichao Ling and Junfeng Lin},
journal= {arXiv preprint arXiv:2003.00334},
year = {2020}
}