Security price dynamics and simulation in financial engineering

Applications in financial engineering have relied heavily on Brownian motion as a workhorse model for pricing derivative securities and implementing risk management programs. When more than one state variable is required, the standard approach is to use a multivariate Brownian motion with constant correlations. This article briefly summarizes several important reasons why this approach is not adequate (and in some cases, can lead to disaster). Examples include fat tails, volatility clustering, large discrete jumps, parameter instability, and asymmetric correlations. Including such features makes analytic modelling less tractable, and potentially makes simulation a more attractive alternative.