Abstract
The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding financial price model is given and investigated. Then, we analyze the statistical behaviors of the Hong Kong Hang Seng Index and the simulative data derived from the financial model by comparison.
Highlights
Financial fluctuation system is one of complex systems, and the statistical behavior of fluctuation of stock price changes has long been a focus of financial research
Recent research is no longer restricted to the traditional areas but concentrated on the more comprehensive domains, leading to the birth of many burgeoning disciplines through the interaction and amalgamation of mathematics and other fields such as finance, biology, and sociology
The study of financial market prices has been found to exhibit some universal properties similar to those observed in interacting particle systems with a large number of interacting units
Summary
Financial fluctuation system is one of complex systems, and the statistical behavior of fluctuation of stock price changes has long been a focus of financial research. The theory of stochastic interacting particle systems see 1–6 recently has been applied to study the behaviors of market fluctuations, see 7–15. A new method is introduced to model and describe the fluctuations of market prices, namely, we use the lattice fractal Sierpinski carpet percolation to establish a new random market price in a financial market. In this financial model, the local interaction or influence among traders in one stock market is constructed, and a cluster of percolation is used to define the cluster of traders sharing the same opinion about the market. The behaviors of long memory and long-range correlation in volatility series of market returns are exhibited
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