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Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options

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  • Todorov, Viktor

Abstract

In this paper, we derive a higher-order asymptotic expansion of characteristic functions of an Itô semimartingale over asymptotically shrinking time intervals. The leading term in the expansion is determined by the value of the diffusive coefficient at the beginning of the interval. The higher-order terms are determined by the jump compensator as well as the coefficients appearing in the diffusion dynamics. The result is applied to develop a nearly rate-efficient estimator of the leverage coefficient of an asset price, i.e., the coefficient in its volatility dynamics that appears in front of the Brownian motion that drives also the asset price.

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  • Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:671-705
    DOI: 10.1016/j.spa.2021.09.005
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    Cited by:

    1. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    2. Todorov, Viktor & Zhang, Yang, 2023. "Bias reduction in spot volatility estimation from options," Journal of Econometrics, Elsevier, vol. 234(1), pages 53-81.
    3. Carsten H. Chong & Viktor Todorov, 2023. "Volatility of Volatility and Leverage Effect from Options," Papers 2305.04137, arXiv.org, revised Jan 2024.
    4. Carsten Chong & Viktor Todorov, 2022. "Short-time expansion of characteristic functions in a rough volatility setting with applications," Papers 2208.00830, arXiv.org.

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