Dynamics of the financial market

Abstract

Financial mathematics must make use of assumptions in the development of mathematical models that provide predictive power on the behavior of economic markets, as it is impossible to collect data on the market as a whole. As a result, important quantities, such as the risk-measurement of a portfolio, are often inaccurately estimated. The financial market seems to be an erratic, pattern-less system. Indeed, attempts to find patterns, and to explain the processes behind the price movements of an asset, have been largely unsuccessful. This is analogous to the ‘Turkey Problem' described by N. Taleb in his book "The Black Swan". To illustrate, a turkey spends its life being fed and raised for slaughter, a fact that is unbeknownst to it. From the point of view of the turkey, life is delicious and predictable, until the day it is killed. For the turkey, its death is a ‘black swan event’, as it represents something highly unpredictable and catastrophic. This same type of uncertainty is also present in financial markets.