Abstract
For the first time, the power law characteristics of stock price jump intervals have been empirically found generally in stock markets. The classical jump-diffusion model is described as the jump-diffusion model with power law (JDMPL). An artificial stock market (ASM) is designed in which an agent’s investment strategies, risk appetite, learning ability, adaptability, and dynamic changes are considered to create a dynamically changing environment. An analysis of these data packets from the ASM simulation indicates that, with the learning mechanism, the ASM reflects the kurtosis, fat-tailed distribution characteristics commonly observed in real markets. Data packets obtained from simulating the ASM for 5010 periods are incorporated into a regression analysis. Analysis results indicate that the JDMPL effectively characterizes the stock price jumps in the market. The results also support the hypothesis that the time interval of stock price jumps is consistent with the power law and indicate that the diversity and dynamic changes of agents’ investment strategies are the reasons for the discontinuity in the changes of stock prices.
Highlights
The jump-diffusion model (Merton, 1976) combines the continuous sample path and the stochastic jump process together with the “abnormal” vibrations described by a “Poisson driven” process [1].Merton’s model has a concise form and clear logic and has become the standard model in analyzing the discontinuous change of the underlying asset price since it was presented
The results support the hypothesis that the time interval of stock price jumps is consistent with the power law and indicate that the diversity and dynamic changes of agents’ investment strategies are the reasons for the discontinuity in the changes of stock prices
We study the power law of the stock price jump interval empirically and experimentally
Summary
The jump-diffusion model (Merton, 1976) combines the continuous sample path and the stochastic jump process together with the “abnormal” vibrations described by a “Poisson driven” process [1]. In order to explain the behavior mechanism of jump intervals, we established an artificial stock market (ASM) and adopted a computational experiment approach to perform financial simulations. Compared with traditional financial economics research, this branch of finance neither advocates the passive observation of data (empirical approaches) nor relies on mathematical models (logic approaches). Rather, it uses specific “experiment” approaches to determine the underlying regularities of financial phenomena [21]. S&P 500 Index’s jump intervals and use the simulation data packets of the ASM to verify and describe the jump-diffusion model with power law (JDMPL) so that the microstructural interpretations are proposed to explain the JDMPL.
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