Time-varying conditional Johnson SU density in value-at-risk (VaR) methodology

Abstract

Stylized facts on financial time series data are the volatility of returns that follow non-normal conditions such as leverage effects and heavier tails leading returns to have heavier magnitudes of extreme losses. Value-at-risk is a standard method of forecasting possible future losses in investments. A procedure of estimating value-at-risk using time-varying conditional Johnson SU¬ distribution is introduced and assessed with econometric models. The Johnson distribution offers the ability to model higher parameters with time-varying structure using maximum likelihood estimation techniques. Two procedures of modeling with the Johnson distribution are introduced: joint estimation of the volatility and two-step procedure where estimation of the volatility is separate from the estimation of higher parameters. The procedures were demonstrated on Philippine-foreign exchange rates and the Philippine stock exchange index. They were assessed with forecast evaluation measures with comparison to different value-at-risk methodologies. The research opens up modeling procedures where manipulation of higher parameters can be integrated in the value-at-risk methodology.Time Varying Parameters; GARCH models; Nonnormal distributions; Risk Management