Abstract
A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GARCH model. It is found that volatility determined by the GARCH model exhibits "volatility clustering" also observed in the real financial markets. Using volatility determined by the GARCH model we examine the mixture-of-distribution hypothesis (MDH) suggested for the asset return dynamics. We find that the returns standardized by volatility are approximately standard normal random variables. Moreover we find that the absolute standardized returns show no significant autocorrelation. These findings are consistent with the view of the MDH for the return dynamics.
Highlights
Statistical properties of asset price returns have been extensively studied and some pronounced properties are found and classified as stylized facts[1]
A possible origin for the fat-tailed distributions has been explained by the mixture-of-distribution hypothesis (MDH)[2] where the price return dynamics is described by a Gaussian random process with time-varying volatility
The volatility of a financial spin model with three-states was investigated by the GARCH model
Summary
Statistical properties of asset price returns have been extensively studied and some pronounced properties are found and classified as stylized facts[1]. One of the stylized facts known for many years is that the probability distributions of returns exhibit fat-tailed distributions. This evidence indicates that asset price dynamics is not a simple Gaussian random walk. It is well known that the volatility changes with time and exhibits persistence of the same magnitude of the volatility This feature of the volatility is called ”volatility clustering” which is one of the stylized facts. Since the invention of the ARCH and GARCH models many extended models have been proposed and applied for empirical finance. After determining the volatility we further examine the view of the MDH for the return dynamics of the financial spin model
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