On An Asset Pricing Model Based On A Nonlinear Function Of Price Expectation

We introduce a reverse parameter by considering the market containing three kinds of traders: the fundamentalists, reverse and forward traders. In view of that the traders in the market are not updating their trading strategies synchronous based on the income information obtained by different types of traders, we introduce a time-varying market fraction that in each time period the fixed percentage of all types of traders update their trading strategies synchronous based on fitness measure. At last we establish an asset pricing model by considering a nonlinear function impacted by the price volatility of the reverse and forward traders. We divide model into several sub models according to the reverse parameter and market fraction, use the theory of difference equation analyze the stability and bifurcation of the model and discuss effect of the reverse parameter on fundamental steady state in pitchfork boundary. Finally,we compare the empirical simulation return data with the existing data in real market and in existing model, and found that they all satisfy the financial data characteristics such as volatility clustering and fat tail. Compared with the existing model, our model fits better with the real market in risk assets return series with the upward trend.