Biblioteca de la Universidad Complutense de Madrid

The Rise and Fall of S&P500 Variance Futures


Chang, Chia-Lin y Jimenez-Martin, Juan-Angel y McAleer, Michael y Pérez Amaral, Teodosio (2011) The Rise and Fall of S&P500 Variance Futures. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 35, 2011, ] (No publicado)

[img] PDF
Creative Commons License
Esta obra está bajo una licencia de Creative Commons: Reconocimiento - No comercial.


URL Oficial:


Volatility is an indispensible component of sensible portfolio risk management. The volatility of an asset of composite index can be traded by using volatility derivatives, such as volatility and variance swaps, options and futures. The most popular volatility index is VIX, which is a key measure of market expectations of volatility, and hence is a key barometer of investor sentiment and market volatility. Investors interpret the VIX cash index as a “fear” index, and of VIX options and VIX futures as derivatives of the “fear” index. VIX is based on S&P500 call and put options over a wide range of strike prices, and hence is not model based. Speculators can trade on volatility risk with VIX derivatives, with views on whether volatility will increase or decrease in the future, while hedgers can use volatility derivatives to avoid exposure to volatility risk. VIX and its options and futures derivatives has been widely analysed in recent years. An alternative volatility derivative to VIX is the S&P500 variance futures, which is an expectation of the variance of the S&P500 cash index. Variance futures are futures contracts written on realized variance, or standardized variance swaps. The S&P500 variance futures are not model based, so the assumptions underlying the index do not seem to have been clearly understood. As these two variance futures are thinly traded, their returns are not easy to model accurately using a variety of risk models. This paper analyses the S&P500 3-month variance futures before, during and after the GFC, as well as for the full data period, for each of three alternative conditional volatility models and three densities, in order to determine whether exposure to risk can be incorporated into a financial portfolio without taking positions on the S&P500 index itself.

Tipo de documento:Documento de trabajo o Informe técnico
Palabras clave:Risk management, Financial derivatives, Futures, options, Swaps, 3-month variance futures, 12-month variance futures, Risk exposure, Volatility.
Materias:Ciencias Sociales > Economía > Finanzas
Ciencias Sociales > Economía > Econometría
JEL:C22, G32, G01
Título de serie o colección:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Código ID:13910

Black, F. (1976), Studies of stock market volatility changes, in 1976 Proceedings of the American Statistical Association, Business & Economic Statistics Section, pp. 177-181.

Bollerslev, T. (1986), Generalised autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327.

Brenner, M., E.Y. Ou and J.E. Zhang (2006), Hedging volatility risk, Journal of Banking and Finance, 30, 811-821.

Caporin, M. and M. McAleer (2010), Model selection and testing of conditional and stochastic volatility models, to appear in L. Bauwens, C. Hafner and S. Laurent (eds.), Handbook on Financial Engineering and Econometrics: Volatility Models and Their Applications, Wiley, New York. Available at SSRN:

Caporin, M. and M. McAleer (2011), Do we really need both BEKK and DCC? A tale of two multivariate GARCH models, to appear in Journal of Economic Surveys.

Chang, C.-L., J.-A. Jimenez-Martin, M. McAleer and T. Perez Amaral (2011), Risk management of risk under the Basel Accord: Forecasting value-at-risk of VIX futures, Managerial Finance, 37, 1088-1206. Available at SSRN:

Chicago Board Options Exchange (2003), VIX: CBOE volatility index, Working paper, Chicago.

Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.

Glosten, L., R. Jagannathan and D. Runkle (1992), On the relation between the expected value and volatility of nominal excess return on stocks, Journal of Finance, 46, 1779-1801.

Huskaj, B. (2009), A value-at-risk analysis of VIX futures: Long memory, heavy tails, and asymmetry. Available at SSRN:

Ishida, I., M. McAleer and K. Oya (2011), Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P500 and VIX, Managerial Finance, 37, 1048-1067.

Li, W.K., S. Ling and M. McAleer (2002), Recent theoretical results for time series models with GARCH errors, Journal of Economic Surveys, 16, 245-269. Reprinted in M. McAleer and L. Oxley (eds.), Contributions to Financial econometrics: Theoretical and Practical Issues, Blackwell, Oxford, 2002, pp. 9-33.

Ling, S. and M. McAleer (2002a), Stationarity and the existence of moments of a family of GARCH processes, Journal of Econometrics, 106, 109-117.

Ling, S. and M. McAleer (2002b), Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models, Econometric Theory, 18, 722-729.

Ling, S. and M. McAleer, (2003a), Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, 19, 278-308.

Ling, S. and M. McAleer (2003b), On adaptive estimation in nonstationary ARMA models with GARCH errors, Annals of Statistics, 31, 642-674.

McAleer, M. (2005), Automated inference and learning in modeling financial volatility, Econometric Theory, 21, 232-261.

McAleer, M., F. Chan and D. Marinova (2007), An econometric analysis of asymmetric volatility: theory and application to patents, Journal of Econometrics, 139, 259-284.

McAleer, M., J.-Á. Jiménez-Martin and T. Pérez-Amaral (2010), Has the Basel II Accord encouraged risk management during the 2008-09 financial crisis?, Available at SSRN:

McAleer, M. and C. Wiphatthanananthakul (2010), A simple expected volatility (SEV) index: Application to SET50 index options, Mathematics and Computers in Simulation, 80, 2079-2090.

Nelson, D.B. (1991), Conditional heteroscedasticity in asset returns: A new approach, Econometrica, 59, 347-370.

Sepp, A. (2008), VIX option pricing in a jump-diffusion model, Risk Magazine, April, 84-89.

Shephard, N. (1996), Statistical aspects of ARCH and stochastic volatility, in O.E. Barndorff-Nielsen, D.R. Cox and D.V. Hinkley (eds.), Statistical Models in econometrics, Finance and Other Fields, Chapman & Hall, London, 1-67.

Whaley, R.E. (1993), Derivatives on market volatility: Hedging tools long overdue, Journal of Derivatives, 1, 71-84.

Zhang, J.E. and Y. Huang (2010), The CBOE S&P500 three-month variance futures, Journal of Futures Markets, 30, 48-70.

Depositado:17 Nov 2011 11:58
Última Modificación:17 Jun 2016 09:21

Sólo personal del repositorio: página de control del artículo