An evolutionary game theory explanation of ARCH effects

Abstract

While ARCH/GARCH equations have been widely used to model financial market data, formal explanations for the sources of conditional volatility are scarce. This paper presents a model with the property that standard econometric tests detect ARCH/GARCH effects similar to those found in asset returns. We use evolutionary game theory to describe how agents endogenously switch among different forecasting strategies. The agents evaluate past forecast errors in the context of an optimizing model of asset pricing given heterogeneous agents. We show that the prospects for divergent expectations depend on the relative variances of fundamental and extraneous variables and on how aggressively agents are pursuing the optimal forecast. Divergent expectations are the driving force leading to the appearance of ARCH/GARCH in the data.JEL Classification: C22, C73, G12, D84

Chaos in the cobweb model with a new learning dynamic

“…, where d parameterizes switching intensity Parke and Waters (2007). use a version of this approach to study heterogeneous expectations with applications to asset pricing.…”

Divergent Behavior in Markets with Idiosyncratic Private Information

“…A fixed point 12 Unlike its biological origins, the RD as employed need not be absorbing at the boundaries as evolution is driven by shifting behavior rather than births and deaths. Parke and Waters (2007) and Guse (2010) preserve the absorbing boundary attribute of RD. solution is n f p such that n f p = f (∆ * (n f p )).…”

Noncausality and asset pricing

“…Chartists act the other way around which may create both positive and negative stock price bubbles even in the absence of random shocks (Brock and Hommes, 1998). Chartists are commonly thought of as technical traders, although Parke and Waters (2007) argue that similar behavior could be observed when agents experiment with different information sets to form expectations. The representative-agent benchmark (6) is nested in the model with fundamentalists and chartists (7-12): The models can be made identical either by setting g C = 0, or n F,t = 1 ∀t.…”

“…Moreover, the fractions of each type of agent in the population can also be interpreted as an omitted variable. Parke and Waters (2007) note that asset prices are generated by a process P t = f (Ω t−1 , n t , ε t ), where Ω t−1 includes all past prices and dividends and n t include the fractions of each type. In this case an econometrician will have access to Ω t−1 , but can not observe behavior or expectations.…”