A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting

Volker Böhm*, Carl Chiarella, Xue Zhong He, Thorsten Hüls

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review

3 Citations (Scopus)


The article investigates the impact of mean-reverting forecasts in a model of asset pricing with two groups of investors under market clearing. Fundamentalists believe that asset prices follow an exogenous stochastic process, while chartists assume that asset prices follow a stochastic geometric decay process. For high values of mean reversion a period-doubling bifurcation occurs followed by a Neimark-Sacker bifurcation, after which homoclinic points exist inducing chaotic dynamics. Before the occurrence of homoclinic points, all orbits induce significant fluctuations with recurring symmetries and nonvanishing autocorrelations in all time series of prices and returns. After the homoclinic bifurcation, prices and returns follow alternating phases with low fluctuations near the steady state followed by phases with large excursions from the steady state. This shows that nonlinearities of the deterministic model rather than random perturbations are the causes of volatility clustering and of the generation of fat tails. Autocorrelations of prices and returns vanish while those of absolute returns and squared returns persist for high-order lags. Thus, the model is able to reproduce some important empirical market features.

Original languageEnglish
Title of host publicationGlobal Analysis of Dynamic Models in Economics and Finance
Subtitle of host publicationEssays in Honour of Laura Gardini
PublisherSpringer-Verlag Berlin Heidelberg
Number of pages28
ISBN (Electronic)9783642295034
ISBN (Print)3642295029, 9783642295027
Publication statusPublished - 1 Mar 2012
Externally publishedYes


  • Asset pricing
  • Autoregressive forecasting
  • Bifurcations
  • Boundedly rational heterogeneous agents
  • Mean reversion


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