Ergodic failure: The key vulnerability in derivatives modelling

Abstract

Ergodicity is a principal property intrinsic to the mathematical modelling of capital markets. It is a structural symmetry underpinning the way in which information is extrapolated from today's state of the world to new, stochastic, future states. The failure of ergodicity — manifested in the myriad of dysfunctionality in capital markets during the financial crisis — represents a primordial breakdown in the way financial engineering has mathematically parameterised its underlying markets. This paper assesses the consequent implications of such failure with respect to the pricing of derivatives.