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COGARCH Models: An Explicit Solution to the Stochastic Differential Equation for Variance

COGARCH Models: An Explicit Solution to the Stochastic Differential Equation for Variance
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Author(s): Yakup Arı (Alanya Alaaddin Keykubat University, Turkey)
Copyright: 2020
Pages: 19
Source title: Emerging Applications of Differential Equations and Game Theory
Source Author(s)/Editor(s): Sırma Zeynep Alparslan Gök (Süleyman Demirel University, Turkey) and Duygu Aruğaslan Çinçin (Süleyman Demirel University, Turkey)
DOI: 10.4018/978-1-7998-0134-4.ch005

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Abstract

In this chapter, the features of a continuous time GARCH (COGARCH) process is discussed since the process can be applied as an explicit solution for the stochastic differential equation which is defined for the volatility of unequally spaced time series. COGARCH process driven by a Lévy process is an analogue of discrete time GARCH process and is further generalized to solutions of Lévy driven stochastic differential equations. The Compound Poisson and Variance Gamma processes are defined and used to derive the increments for the COGARCH process. Although there are various parameter estimation methods introduced for COGARCH, this study is focused on two methods which are Pseudo Maximum Likelihood Method and General Methods of Moments. Furthermore, an example is given to illustrate the findings.

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