A Microeconomic Approach to Diffusion Models For Stock Prices

This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete-time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous-time model. the resulting process is an Ornstein-Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case. Copyright 1993 Blackwell Publishers.

[1]  Alan Kirman,et al.  Ants, Rationality, and Recruitment , 1993 .

[2]  Philip Protter,et al.  FROM DISCRETE- TO CONTINUOUS-TIME FINANCE: WEAK CONVERGENCE OF THE FINANCIAL GAIN PROCESS' , 1992 .

[3]  P. Protter,et al.  Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations , 1991 .

[4]  R. C. Witt,et al.  Relevant Distributions for Insurance Prices in an Arbitrage Free Equilibrium , 1991 .

[5]  P. Protter,et al.  Stochastic Analysis: Characterizing the weak convergence of stochastic integrals , 1991 .

[6]  Richard H. Day,et al.  Bulls, bears and market sheep , 1990 .

[7]  L. Summers,et al.  Noise Trader Risk in Financial Markets , 1990, Journal of Political Economy.

[8]  Daniel B. Nelson.  ARCH models as diffusion approximations , 1990 .

[9]  P. Protter.  Stochastic integration and differential equations , 1990 .

[10]  L. Slominski.  Stability of strong solutions of stochastic differential equations , 1989 .

[11]  L. Summers,et al.  Positive Feedback Investment Strategies and Destabilizing Rational Speculation , 1989 .

[12]  Kenneth A. Froot,et al.  Exchange Rate Dynamics Under Stochastic Regime Shifts: a Unified Approach , 1989 .

[13]  Charles Goodhart,et al.  The Foreign Exchange Market: A Random Walk with a Dragging Anchor , 1988 .

[14]  V. Smith,et al.  Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets , 1988 .

[15]  K. West,et al.  Bubbles, Fads, and Stock Price Volatility Tests: a Partial Evaluation , 1988 .

[16]  M. Barnsley,et al.  A new class of markov processes for image encoding , 1988, Advances in Applied Probability.

[17]  Fischer Black,et al.  Simplifying portfolio insurance , 1987 .

[18]  Avi Bick,et al.  On the Consistency of the Black-Scholes Model with a General Equilibrium Framework , 1987, Journal of Financial and Quantitative Analysis.

[19]  Sanford J. Grossman,et al.  An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies , 1987 .

[20]  David M. Kreps,et al.  Price Destabilizing Speculation , 1986, Journal of Political Economy.

[21]  L. Summers.  Does the Stock Market Rationally Reflect Fundamental Values , 1986 .

[22]  A. Brandt.  The stochastic equation Yn+1=AnYn+Bn with stationary coefficients , 1986 .

[23]  Jeffrey A. Frankel,et al.  The Dollar as an Irrational Speculative Bubble: A Tale of Fundamentalists and Chartists , 1986 .

[24]  J. Tirole.  On the Possibility of Speculation under Rational Expectations , 1982 .

[25]  Alain Monfort,et al.  Rational Expectations in Dynamic Linear Models: Analysis of the Solutions , 1982 .

[26]  David M. Kreps.  Multiperiod Securities and the Efficient Allocation of Risk: A Comment on the Black-Scholes Option Pricing Model , 1982 .

[27]  H. Föllmer.  Random economies with many interacting agents , 1974 .

[28]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[29]  Milton C. Chew.  Distributions in Statistics: Continuous Univariate Distributions-1 and 2 , 1971 .

[30]  S. Orey,et al.  ANALYTICAL TREATMENT OF ONE‐DIMENSIONAL MARKOV PROCESSES , 1971 .

[31]  D. Laidler.  The demand for money , 1969 .

[32]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .