Global and microstructural ergodic properties of financial markets*

In finance everyone is concerned about future expectations. Whether it's pricing or risk evaluation - current models always involve some form of time averaging. Understanding the ergodic properties of the markets allows to replace the time average with ensemble average. Since calculation of ensemble average requires only one step in time, this approach allows much faster computation, and therefore a much faster reaction to changing market conditions.
In this work we will explore market ergodicity from various points of view. First, we will consider market properties as a global dynamic system made of individual securities. Second, we will discuss ergodicity of individual securities represented by a dynamic limit order book. We will show how concepts of ergodicity can be applied to determine current market volatility, and introduce the new eVOL and eVAR indices that measure current volatility as opposed to traditional realized and implied volatilities. We will demostrate real-life examples highlighting the capabilities of these new indices for trading and asset management.