Modelling the Value of the S&P 500 - A System Dynamics Perspective

Abstract

This paper seeks to model the adjustment process in the stock market by a continuous time state space model focusing on input-out relations. The value of the S&P 500 is generated as the output of the model with earnings and the interest rate as input. The model is found to fit the data well, and indicates that the stock price dynamics can be considered as a price-following-value process. The value determines the time varying trend of price, and random buy-sell pressure drives price fluctuations about value. The 1987 stock price bubble shows up clearly as a gap between price and value.

Solving the Price-Earnings Puzzle

“…Even so, we still remain on the lookout for better models. In reality, the performance of the dynamic model in Chiarella and Gao (2002b) is better than regression models.…”

“…Since EY ≈ R, substituting the interest rate R for the earnings yield EY, time series data show that E / R is highly correlated to the stock price P, ie P = E / EY ≈ E / R. Financial practitioners use this information to predict the aggregate stock market in practice (see Wigmore, 1998). Chiarella and Gao (2002b) have shown how the process of earnings yield following interest rate may be considered as the basic adjustment process of the stock market, and have specified and estimated a dynamic model to express this adjustment process. It is the underlying adjustment mechanism that guarantees the long run equilibrium between the earnings yield and interest rates.…”

Generalized Multinomial CRR Option Pricing Model and its Black-Scholes type limit

“…For some time past and as documented in considerable number of papers [1], [2], [24], [34], [35], [40], [46], [50], [70], [29], [18] written by academics and practitioners, both normality and continuity assumptions are contradicted by the most of real data.…”