Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model

Abstract

The behavioral origins of the stylized facts of financial returns have been addressed in a growing body of agent-based models of financial markets. While the traditional efficient market viewpoint explains all statistical properties of returns by similar features of the news arrival process, the more recent behavioral finance models explain them as imprints of universal patterns of interaction in these markets. In this paper we contribute to this literature by introducing a very simple agent-based model in which the ubiquitous stylized facts (fat tails, volatility clustering) are emergent properties of the interaction among traders. The simplicity of the model allows us to estimate the underlying parameters, since it is possible to derive a closed form solution for the distribution of returns. We show that the tail shape characterizing the fatness of the unconditional distribution of returns can be directly derived from some structural variables that govern the traders' interactions, namely the herding propensity and the autonomous switching tendency.

Heterogeneous expectations in the gold market: Specification and estimation

“…Other 'indirect' estimation methods include the use of filtering techniques (see Baak, 1999, Chavas, 2000 and simulation based estimation such as those employed in Winker (2001, 2003) and Winker and Gilli (2004). Furthermore, Alfarano et al (2005Alfarano et al ( , 2006 take advantage of a derived closed-form expression for the stationary distribution of returns for a particular class of HAM to estimate the distribution of agents within a given market.…”

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

“…Defining a (moment-specific) bootstrapped p-value to quantify a model's goodness-of-fit, it turns out that roughly one-third of all simulation runs cannot be directly rejected by the data. On the other hand, the joint MCR amounts to more than 25 per cent, which we think is a fairly respectable order of 3 See Gilli and Winker (2003), Alfarano et al (2005), Manzan and Westerhoff (2007), Winker et al (2007), Boswijk et al (2007), Amilon (2008), Franke (2009), Li et al (2010), Chiarella et al (2011), Franke and Westerhoff (2011). 4 The choice of MSM does not rule out that also other estimation approaches may be tried.…”

Testing of a market fraction model and power-law behaviour in the DAX 30

“…Lux and Marchesi (1999) argue that the indeterminateness of the market fractions in a market equilibrium and the dependence of stability on the market fractions exist in a broad class of behavioural finance models, which is further supported by Giardina and Bouchaud (2003) and Lux and Schornstein (2005). observed mispricing) and noise traders (who follow the mood of the market), Alfarano et al (2005) show that their herding model is able to produce relatively realistic time series for returns whose distributional and temporal characteristics are astonishingly close to the empirical findings. This is partly due to a bi-modal limiting distribution for the fraction of noise traders in the optimistic and pessimistic groups of individuals and partly due to the stochastic nature of the process leading to recurrent switches from one majority to another.…”

“…Boswijk et al (2007) derive a reduced form equation from a simplified Hommes (1997, 1998) type model and estimate it by using nonlinear least square method. Alfarano et al (2005) estimate a simplified herding model by maximum likelihood method. Amilon (2008) estimates two specifications of the extended Brock and Hommes switching models described in De Grimaldi (2003, 2006) by using the efficient method of moments and maximum likelihood method.…”