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Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model

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  • Cecilia Mancini

Abstract

We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity λ>0, and we consider the process Y such that Y0∈ℝ and where a, σ are predictable bounded stochastic processes, and γ is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y0, Yt1, …, Ytn−1, Ytn} is available, with ti=ih. Using such observations, we construct estimators of Nti, i=1, …, n, λ and γτj, where τj are the instants of jump within [0, nh]. They are consistent and asymptotically controlled when the number of observations increases and the step h tends to zero.

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  • Cecilia Mancini, 2004. "Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2004(1), pages 42-52.
    • Handle: RePEc:taf:sactxx:v:2004:y:2004:i:1:p:42-52
    DOI: 10.1080/034612303100170091
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    Cited by:

    1. Shin, Minseok & Kim, Donggyu & Fan, Jianqing, 2023. "Adaptive robust large volatility matrix estimation based on high-frequency financial data," Journal of Econometrics, Elsevier, vol. 237(1).
    2. Donggyu Kim & Minseog Oh, 2024. "Dynamic Realized Minimum Variance Portfolio Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1238-1249, October.
    3. Donggyu Kim & Minseog Oh, 2024. "Dynamic Realized Minimum Variance Portfolio Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1238-1249, October.

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