Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Testing for a unit root in a process exhibiting a structural break in the presence of GARCH errors

This paper considers the effect of GARCH errors on the tests proposed byPerron (1997) for a unit root in the presence of a structural break. We assessthe impact of degeneracy and integratedness of the conditional varianceindividually and find that, apart from in the limit, the testing procedure isinsensitive to the degree of degeneracy but does exhibit an increasingover-sizing as the process becomes more integrated. When we consider the GARCHspecifications that we are likely to encounter in empirical research, we findthat the Perron tests are reasonably robust to the presence of GARCH and donot suffer from severe over-or under-rejection of a correct null hypothesis.

American option valuation: implied calibration of GARCH pricing models

This study analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.