On GARCH Models and Applications: Foreign Exchange Rate Volatility and a Price Index


  • Abdelali Ezzebsa LMAM Laboratory, 8 May 1945 University, Guelma, Algeria
  • Sihem Nedjar LaPS Laboratory, Badji-Mokhtar-Annaba University, Annaba, Algeria
  • Halim Zeghdoudi LaPS Laboratory, Badji-Mokhtar-Annaba University, Annaba, Algeria


Volatility swaps, Heston model, GARCH, ARCH, forecasting


This paper studies the benefit of GARCH models, and presents two applications on the exchanging of the rate volatility of Algerian Dinar against the Euro and US Dollar and CAC40French index. The goal of this work is to add another benefit of univariate GARCH models which this work contains an application relates to exchange rates between the Algerian Dinar (DZD), the American dollar (USD) and the Euro from 1/01/2014 to 15/05/2019. Also, this paper applies analytical solutions from Zeghdoudi et al. (2014) to price a swap on the volatility of the CAC40 French index for five years (from October 2013 to April 2018).


Amrani M, Zeghdoudi H. Benefit of GARCH multivariate models: application to the energy market. Asian J Prob Stat. 2021; 13(4): 1-11.

Bollerslev T. Generalized autorregressive conditional heteroskedasticity. J Econometrics. 1986; 31(3): 307-327.

Brockhaus O, Long D. Volatility swaps made simple. Risk. 2000; 92-96.

Brooks C. GARCH Modelling in finance: A review of the software options. Econ J.1997; 107(443): 1271-1276.

Brooks C, Burke SP. Forecasting exchange rate volatility using conditional variance models selected by information criteria. Econ Lett. 1998; 61(3): 273-278.

Demeterfi K, Derman E, Kamal M, Zou J. A guide to volatility and variance swaps. J Deriv. 1999; 6(4): 9-32.

Engle RF. Autorregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica. 1982; 50(4): 987-1007.

Engle R, Lilien DM, Robins RP. Estimating time varying risk premia in the term structure: the ARCH-M model. Econometrica. 1987; 55(2): 391-407.

Engle R. Jeffrey R. Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model. J Empi Fin. 1997; 4(3): 187-212.

Ezzebsa A, Zeghdoudi H, Remita MR, Nedjar S. Around ARCH/GARCH models and their application to exchange rate volatility. Int J Stat Econ. 2013; 11(2): 44-60.

Heston SL. A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev Financ Stud. 1993; 6(2): 327-343.

Hopper GP. What determines the exchange rate: economics factors or market sentiment. Bus Rev.1997; 17-29.

Javaheri A. The volatility process: a study of stock market dynamics via parametric stochastic volatility models and a comparaison to the information embedded in the option price. Humanities and Social Sciences. PhD [dissertation]. École Nationale Supérieure des Mines de Paris; 2004.

Priviledge C. Stock market volatility using GARCH models: Evidence from South Africa and China stock markets. J Econ Beh Stud. 2016; 8(6): 237-245.

Tuckman B. Fixed income securities: tools for today’s markets. New York: John Wiley and Sons; 1996.

Weiss AA. Asymptotic theory for ARCH models: estimation and testing. Econ Theory. 1986: 2(1): 107-131.

West K, Cho D. The predictive ability of several models of exchange rate volatility. J Econometrics. 1995; 69(2): 367-391.

Zakoian JM. Threshold ARCH models, CREST, INSEE, Paris; 1991.

Zakoian JM. Threshold heteroscedastic models. J Econ Dynam Contr. 1994; 18(5): 931-955.

Zeghdoudi H, Boudjaada L, Tlaidjia N. Use of the artificial neural networks (ANNs) to guiding the financial decisions: exchange rate volatility of Algerian Dinar. Int Res J Fin Econ. 2013; 115: 87-94.

Zeghdoudi H, Lallouche A, Remita MR. On volatility swaps for stock market forecast: application example CAC40 French index. J Prob Stat. 2014; 1-6.

Zeghdoudi H, Bouseba FZ. Use of the GARCH models to energy markets: oil price volatility. Glob J Pure App Math. 2015; 11(6): 4385-4394.




How to Cite

Ezzebsa, A. ., Nedjar, S. ., & Zeghdoudi, H. . (2023). On GARCH Models and Applications: Foreign Exchange Rate Volatility and a Price Index. Thailand Statistician, 21(4), 812–823. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/251061