안정성 조건을 고려한 GARCH계열 모형의 구현에 관한 연구

Abstract

This paper introduces the specifications of various GARCH-family models under both physical probability measure (P-measure) and risk-neutral probability measure (Q-measure) and explains how researchers can implement the models using high-level programming languages such as MATLAB. The stability conditions of the GARCH-family models tend to become more complicated under the Q-measure and these conditions should be considered during the estimation stage to obtain reliable parameter estimates. Unfortunately, however, existing statistical analysis packages only provide users the final estimation results and the users can obtain the estimates based on the historical observation under the P-measure. For the successful application of the GARCH-family models to various fields of financial engineering (e.g., option pricing and risk management) and for the expandability of the models, the implementation of the estimation procedure based on the programming languages is necessary and quite useful. We suggest the programming methodology that enforces the GARCH parameters to satisfy the non-negativity and stability conditions when we implement the MLE (Maximum Likelihood Estimation) and the NLSE (Nonlinear Least Square Estimation) techniques.