A GARCH with Time-Changed Lévy Innovation Model and Its Applications from an Economic Perspective

Abstract

The paper constructs a GARCH process with time-changed Lévy innovations from the economic perspective which assumes that the arrival of new information causes the asset return to be stochastic and volatility clustering. The GARCH (1,1) process with generalized hyperbolic innovation is introduced as a general form for the volatility process. The paper uses a special case of the process to discuss the economic meaning behind alternative dynamic behaviors, and then applies it in pricing a European option under the hypothesis that every investor selects the canonic martingale measure.