2020/02/29 by Nian Yao, Zhiqiu Li, Yao, Nian +5
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #q-fin.CP #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2003.00334
openalex publication_date 2020/02/29 · arxiv created 2020/05/08 · arxiv updated 2020/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Gärtner-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.