This assignment will discuss the application of GARCH technique on modelling financial risks. GARCH model is a time series model consisting autocorrelation for the volatility. It is often used to model financial volatility as its pattern accords with the clustering volatility of financial data. GARCH indicates that the forecast variance is based on recent observations of the variance and the recent observations of squared average. It assumes that the variance tends to be dragged back to the long-run average level.
2. Reasons for using GARCH in financial risk modelling
Volatility in financial data commonly exhibit clustering, where there are periods of high variance and periods of low variance. The chance of clustering is larger near large changes, and vice versa. Thus, GARCH incorporates the clustering behaviour and has heavier tails than normal distribution. In addition, GARCH model also models for ‘black swan’ events. However, one limitation of GARCH is that it cannot model asymmetric volatilities. That is, GARCH ignores the sign of past volatility and negative shocks will have the same effect of positive shocks. However, in reality, the negative shocks often have larger impact than positive ones. This is referred to as leverage effect (Engle and Siriwardane, 2014), and can be modelled by some extension models of GARCH, e,g, TGARCH or EGARCH.
3. Credit risk modelling using GARCH
There are many credit risk modelling techniques involving GARCH. However, in academic researches and financial institutional reviews, GARCH model is seldom directly used to model credit risk. The most common used method to model credit risk involving GARCH is the combination of Merton’s credit risk model and the GARCH volatility model. Two approaches are commonly used. The first is the reduction approach, deriving credit risk directly from price of corporate bonds, and use Poisson process to model the firm’s default. The second is the Merton model, which considers the capital structure of firms and models default as events occurring when firm’s value fall behind a certain amount. The model is complicated derived from the Black and Scholes’ option pricing model (Rohde and Sibbertsen, 2014). Another commonly used model for credit risk modelling is the KMV model, which also involves modelling the asset value and the asset volatility.
The GARCH in both cases are to model the price volatility. In the first approach, it can use GARCH to model the bond price volatility and then deriving the credit risk. In the Merton model, it could use GARCH to model the stock price volatility. Thus, in the Merton Credit Risk Model context, the modelling of credit risk has been converted into a problem of modelling market risk, particularly, the stock price volatility. In the last case, the KMV model, the nature of the modelling is to model the market risk (Ajibola et al, 2013).
Therefore, it is argued that for the use of GARCH model to model credit risk,...