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Asymptotic Smiles for an Affine Jump-Diffusion Model

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  • Nian Yao
  • Zhiqiu Li
  • Zhichao Ling
  • Junfeng Lin

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.

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  • Nian Yao & Zhiqiu Li & Zhichao Ling & Junfeng Lin, 2020. "Asymptotic Smiles for an Affine Jump-Diffusion Model," Papers 2003.00334, arXiv.org, revised May 2020.
    • Handle: RePEc:arx:papers:2003.00334
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    References listed on IDEAS

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