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Statistical properties and economic implications of jump-diffusion processes with shot-noise effects

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  • Moreno, Manuel
  • Serrano, Pedro
  • Stute, Winfried

Abstract

The shot-noise jump-diffusion (SNJD) model aims to reflect how economic variables respond to the arrival of sudden information. This paper analyzes the SNJD model, providing its statistical distribution and closed-form expressions for the characteristic function and moments. We also analyze the dynamics of the model, concluding that the degree of serial autocorrelation is related to the occurrence and magnitude of abnormal information. In addition, we provide some useful approximations in a particular case that considers exponential-type decay. Empirically, we propose a GMM approach to estimate the parameters of the model and present an empirical application for the stocks included in the Dow Jones Averaged Index. Our findings seem to confirm the presence of shot-noise effects in 73% of the stocks and a strong relationship between the shot-noise process and the autocorrelation pattern embedded in data.

Suggested Citation

  • Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:656-664
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    1. Claude DIEBOLT & Tapas MISHRA & Mamata PARHI, 2015. "A "Jump" in the Stochasticity of the Solow-Swan Growth Model," Economies et Sociétés (Serie 'Histoire Economique Quantitative'), Association Française de Cliométrie (AFC), issue 50, pages 905-917, Juin.
    2. Thorsten Schmidt, 2016. "Shot-Noise Processes in Finance," Papers 1612.06616, arXiv.org.
    3. Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.
    4. Oleksandra Putyatina & Jörn Sass, 2018. "Approximation for portfolio optimization in a financial market with shot-noise jumps," Computational Management Science, Springer, vol. 15(2), pages 161-186, June.
    5. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    6. Ji, Jingru & Wang, Donghua & Xu, Dinghai & Xu, Chi, 2020. "Combining a self-exciting point process with the truncated generalized Pareto distribution: An extreme risk analysis under price limits," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 52-70.
    7. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    8. Fu, Jun & Yang, Hailiang, 2012. "Equilibruim approach of asset pricing under Lévy process," European Journal of Operational Research, Elsevier, vol. 223(3), pages 701-708.
    9. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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    More about this item

    Keywords

    Finance Shot-noise Characteristic function Generalized method of moments;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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