Irfan Ahmed, PhD

MODELLING VOLATILITY An Excursion into Non-linearity Land l   Motivation : the linear structural (and time series) models cannot explain a number of important features common to such financial data                 - leptokurtosis                 - volatility clustering or volatility pooling                 - leverage effects  l   Our “traditional” structural model could be something like:                   y t = b 1 + b 2 x 2 t + ... + b k x kt + u t, or more compactly   y = X b + u. Non-linear Models: A Definition l   Campbell, Lo and MacKinlay (1997) define a non-linear data generating process as one that can be written                                 y t = f ( u t , u t -1 , u t -2 , …)                 where u t is an iid error term and f is a non-linear function. l   They also give a slightly more specific definition as                                 y t = g ( u t -1 , u t -2 , …)+ u t s 2 ( u t -1 , u t -2 , …)                    where g is a function of past error te