Research Article On Volatility Swaps for Stock Market Forecast: Application Example CAC 40 French Index Halim Zeghdoudi, 1,2 Abdellah Lallouche, 3 and Mohamed Riad Remita 1 1 LaPS Laboratory, Badji-Mokhtar University, BP 12, 23000 Annaba, Algeria 2 Department of Computing Mathematics and Physics, Waterford Institute of Technology, Waterford, Ireland 3 Universit´ e 20 Aout, 1955 Skikda, Algeria Correspondence should be addressed to Halim Zeghdoudi; hzeghdoudi@yahoo.fr Received 3 August 2014; Revised 21 September 2014; Accepted 29 September 2014; Published 9 November 2014 Academic Editor: Chin-Shang Li Copyright © 2014 Halim Zeghdoudi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper focuses on the pricing of variance and volatility swaps under Heston model (1993). To this end, we apply this model to the empirical fnancial data: CAC 40 French Index. More precisely, we make an application example for stock market forecast: CAC 40 French Index to price swap on the volatility using GARCH(1,1) model. 1. Introduction Black and Scholes’ model [1] is one of the most signifcant models discovered in fnance in XXe century for valuing liquid European style vanilla option. Black-Scholes model assumes that the volatility is constant but this assumption is not always true. Tis model is not good for derivatives prices founded in fnance and businesses market (see [2]). “Te volatility of asset prices is an indispensable input in both pricing options and in risk management. Trough the introduction of volatility derivatives, volatility is now, in efect, a tradable market instrument” Broadie and Jain [3]. Volatility is one of the principal parameters employed to describe and measure the fuctuations of asset prices. It plays a crucial role in the modern fnancial analysis concerning risk management, option valuation, and asset allocation. Tere are diferent types of volatilities: implied volatility, local volatility, and stochastic volatility (see Baili [4]). To this end, the new fnancial products are variance and volatility swaps, which play a decisive role in volatility hedging and speculation. Investment banks, currencies, stock indexes, fnance, and businesses markets are useful for vari- ance and volatility swaps. Volatility swaps allow investors to trade and to control the volatility of an asset directly. Moreover, they would trade a price index. Te underlying is usually a foreign exchange rate (very liquid market) but could be as well a single name equity or index. However, the variance swap is reliable in the index market because it can be replicated with a linear combination of options and a dynamic position in futures. Also, volatility swaps are not used only in fnance and businesses but in energy markets and industry too. Te variance swap contract contains two legs: fxed leg (variance strike) and foating leg (realized variance). Tere are several works which studied the variance swap portfolio theory and optimal portfolio of variance swaps based on a variance Gamma correlated (VGC) model (see Cao and Guo [5]). Te goal of this paper is the valuation and hedging of volatility swaps within the frame of a GARCH(1,1) stochastic volatility model under Heston model [6]. Te Heston asset process has a variance that follows a Cox et al. [7] process. Also, we make an application by using CAC 40 French Index. Te structure of the paper is as follows. Section 2 considers representing the volatility swap and the variance swap. Section 3 describes the volatility swaps for Heston model, gives explicit expression of  2  , and discusses the relationship between GARCH and volatility swaps. Finally, we make an application example for stock market forecast: CAC 40 French Index using GARCH/ARCH models. Hindawi Publishing Corporation Journal of Probability and Statistics Volume 2014, Article ID 854578, 6 pages http://dx.doi.org/10.1155/2014/854578