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How sensitive are equilibrium pricing models to real-world distortions?

Harbir Lamba

posted on 05 October 2010

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In both finance and economics, quantitative models are usually studied as isolated mathematical objects --- most often defined by very strong simplifying assumptions concerning rationality, efficiency and the existence of disequilibrium adjustment mechanisms. This raises the important question of how sensitive such models might be to real-world effects that violate the assumptions. We show how the consequences of rational behavior caused by perverse incentives, as well as various irrational tendencies identified by behavioral economists, can be systematically and consistently introduced into an agent-based model for a financial asset. This generates a class of models which, in the special case where such effects are absent, reduces to geometric Brownian motion --- the usual equilibrium pricing model. Thus we are able to numerically perturb a widely-used equilibrium pricing model market and investigate its stability. The magnitude of such perturbations in real markets can be estimated and the simulations imply that this is far outside the stability region of the equilibrium solution, which is no longer observed. Indeed the price fluctuations generated by endogenous dynamics, are in good general agreement with the excess kurtosis and heteroskedasticity of actual asset prices. The methodology is presented within the context of a financial market. However, there are close links to concepts and theories from both micro- and macro-economics including rational expectations, Soros' theory of reflexivity, and Minsky's theory of financial instability.