Theory of Financial Risk: Basic notions in probability

TL;DR

This paper introduces fundamental probability concepts relevant to financial risk management, highlighting limitations of classical models and emphasizing the importance of advanced statistical tools for better risk assessment.

Contribution

It provides a concise overview of key probability theories applicable to finance, addressing the shortcomings of Gaussian assumptions in risk estimation.

Findings

Classical models often underestimate true financial risks.

Advanced statistical tools improve risk measurement accuracy.

Introduction to Random Matrix Theory for financial applications.

Abstract

Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on simplified assumptions -- such as Gaussian statistics -- and lead to a systematic (and sometimes dramatic) underestimation of real risks. We summarize a few basic notions in probability theory which are useful in a financial context: Statistics of Extremes, Sums of Random Variables, Central Limit Theorems and Deviations, Correlations and Dependence, and a brief introduction to Random Matrix Theory. This self-contained text corresponds to the first chapter of our book, `Theory of Financial Risk'.