Abstract
Following a Geometrical Brownian Motion extension into an Irrational fractional Brownian Motion model, we re-examine agent behaviour reacting to time dependent news on the log-returns thereby modifying a financial market evolution. We specifically discuss the role of financial news or economic information positive or negative feedback of such irrational (or contrarian) agents upon the price evolution. We observe a kink-like effect reminiscent of soliton behaviour, suggesting how analysts' forecasts errors induce stock prices to adjust accordingly, thereby proposing a measure of the irrational force in a market.
Highlights
A recent paper by Dhesi et al [1] about modelling returns distributions for financial market indices, uses a quite innovative approach for obtaining a better fit. This is achieved by adding an extra stochastic function incorporating a weighting factor over the well known Geometric Brownian Motion (GBM)
It can be recalled that Bulkley and Harris [2] showed that stock price volatility may be due to a failure of the market to form rational expectations, using data on analysts' expectations of long run earnings growth for individual companies
It can be claimed that the model makes a fully pertinent connection between the extra function and irrational behaviour of financial markets
Summary
A recent paper by Dhesi et al [1] about modelling returns distributions for financial market indices, uses a quite innovative approach for obtaining a better fit. Simulations provided (on various data sets) in the Dhesi et al paper [1] show that this model, for describing agent behaviours, lead to very good fits (tested by χ2 tests) to the empirical returns distributions of various empirical price indices. It can be claimed that the model makes a fully pertinent connection between the extra function and irrational behaviour of financial markets.
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