Model misspecification in Financial Risk Management

Abstract

Model risk has become more relevant over the past few decades. A few reasons that attribute to the rise in awareness and interest in model risk include the requirement of advanced risk models by financial sector authorities, the increasing complexity of models deployed, and the vast range of risk types that models impact. Model risk occurs when a financial model is performing inadequately given the data, such that it leads to inappropriate results. Model misspecification is one component of model risk, which refers to violation of necessary model assumptions. A variety of financial risk categories are impact by model misspecification. Among these financial risks are market risk which is the risk arising from the fluctuations of financial asset prices. This study aims to evaluate the impact of model misspecification in Financial Risk Management with our primary focus being on market risk. We identify Generalized Autoregressive Conditional Heteroscedastic (GARCH) as our modelling technique because it is useful in assessing risk and expected returns for assets that display clustered periods of volatility in returns. GARCH is a statistical modelling technique used to assess, analyse and forecast the volatility of returns on financial time series data. GARCH models have become significant tools in the assessment of time series data, largely the traditional normal distribution of GARCH models, because of its ease of use in practice. However, it is proven that high frequency financial data have heavy tails leading to the resulting estimates being inefficient. The Student-t and General error (GED) distributions are more capable of representing these financial series. In this study, we consider the GARCH (1,1) with Normal, Student-t and GED innovations and varying sample sizes. We conduct a series of simulations for the GARCH (1,1) model with the error terms following a Normal distribution. The return series of Samsung electronics daily stock prices, Bitcoin-USD daily cryptocurrency and Moody's seasoned Aaa corporate bond yield (BAAA) are fitted to the GARCH (1,1) with Normal, Student-t and GED innovations. We investigate if these models are subject to model misspecification

when the error terms do not assume similar distributions as the simulated data and real data innovations.