ISSN: 2056-3736 (Online Version) | 2056-3728 (Print Version)

Relationships among US S&P500 Stock Index, its Futures and NASDAQ Index Futures with Volatility Spillover and Jump Diffusion: Modeling and Hedging Performance

Hsiang-Hsi Liu and Yu-Cheng Lin

Correspondence: Hsiang-Hsi Liu, hsiang@mail.ntpu.edu.tw

National Taipei University, Taiwan

pdf (1948.07 Kb) | doi: https://doi.org/10.47260/bae/818

Abstract

This study takes the US S&P500 stock index cash, futures and NASDAQ stock index futures as the main research objects, and applies the ARJI (autoregressive jump intensity model) VEC GJR-GARCH model to examine the co-integration, volatility spillover, jump behavior and hedge performance of the three markets. With the rapid circulation of new information, the financial market will often fluctuate under the impact of new information. Investors will have different and timely responses to emergencies, and this event will have an impact on the stock market. When the event is unexpected or abnormal, the financial market will have huge fluctuations, and this kind of fluctuation is a jump. The empirical results found that the three markets have linkages and volatility spillover effects, and there are indeed discontinuous jumps. Two-way volatility spillovers between S&P500 index cash and futures, and only one-way volatility spillovers from S&P500 futures to the Nasdaq futures market. International investors need to consider information from their own-market volatility (risk) as well as information on volatility spillovers (risk) from other markets. The jump frequency is not a fixed constant, that is, the jump frequency (strength) generated by abnormal information changes over time. In addition, the results of this research also found that the ARJI VEC GJR-GARCH model can better capture the risk of fluctuations in price discontinuities after adding jump factors to the hedging performance estimated by the ARJI VEC GJR-GARCH model. The hedging performance can be more effective, which is conducive to investors' risk management decisions. Also, the performance of direct hedging that is better than the performance of cross hedging.

Keywords:

  Jump Intensity, Jump Size, Co-integration, ARJI, VEC GJR-GARCH, Hedging Ratio, Hedging Performance.


References

Andersen, T. G., Benzoni, L. and Lund, J. (2002). An empirical investigation of continuous‐time equity return models. The Journal of Finance, 57(3), 1239-1284.Bates, D. S. (1991). The crash of ʼ87: was it expected? The evidence from options markets. The Journal of Finance, 46(3), 1009-1044.Berndt, E. R., Hall, B. H., Hall, R. E. and Hausman, J. A. (1974). Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3, 653-665Bertus, M., Godbey, J. and Hilliard, J. E. (2009). Minimum variance cross hedging under mean‐reverting spreads, stochastic convenience yields, and jumps: Application to the airline industry. Journal of Futures Markets, 29(8), 736-756.Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.Chan, W. H. and Maheu, J. M. (2002). Conditional jump dynamics in stock market returns. Journal of Business and Economic Statistics, 20(3), 377-389.Chan, W. H. and Young, D. (2006). Jumping hedges: An examination of movements in copper spot and futures markets. Journal of Futures Market, 26(2), 169-188.Cheang, G. H., Chiarella, C. and Ziogas, A. (2013). The representation of American options prices under stochastic volatility and jump-diffusion dynamics. Quantitative Finance, 13(2), 241-253.Craine, R., Lochstoer, L. A. and Syrtveit, K. (2000). Estimation of a stochastic-volatility jump-diffusion model. Revista de Analisis Economico, 15(1), 61-87.Creel, M. and Kristensen, D. (2015). ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models. Journal of Empirical Finance, 31, 85-108.Das, S. R. (2002). The surprise element: jumps in interest rates. Journal of Econometrics, 106(1), 27-65.Ederington, L. H. (1979). The hedging performance of the new futures markets. The Journal of Finance, 34(1), 157-170.Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007.Engle, R. F. and Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The Journal of Finance, 48(5), 1749-1778.Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. The Journal of Finance, 59(3), 1367-1403.Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38(1), 34-105.Fan, C., Luo, X. and Wu, Q. (2017). Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market. International Review of Economics and Finance, 49, 1-16.Fortune, P. (1999). Are stock returns different over weekends? A jump diffusion analysis of the weekend effect. New England Economic Review, 10, 3-19.Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801.Johnson, L. L. (1960). The theory of hedging and speculation in commodity futures. Review of Economic Studies, 27: 139-151.Kaeck, A. and Alexander, C. (2012). Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions. Journal of Banking and Finance, 36(11), 3110-3121.Koulis, A., Kaimakamis, G. and Beneki, C. (2018). Hedging effectiveness for international index futures markets. Economics and Business, 32(1), 149-159.Lai, Y. S. (2019). Evaluating the hedging performance of multivariate GARCH models. Asia Pacific Management Review, 24(1), 86-95.Liu, Q., Chng, M. T. and Xu, D. (2014). Hedging industrial metals with stochastic volatility models. Journal of Futures Markets, 34(8), 704-730.Maheu, J. M. and McCurdy, T. H. (2004). News arrival, jump dynamics, and volatility components for individual stock returns. The Journal of Finance, 59(2), 755-793.Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7: 77-91.Press, S. J. (1967). A compound events model for security prices. Journal of business, 317-335.Stein, J. L. (1961). The Simultaneous determination of spot and futures prices. The American Economic Review, 51(5), 1012-1025.Todorov, V. (2009). Estimation of continuous-time stochastic volatility models with jumps using high-frequency data. Journal of Econometrics, 148(2), 131-148.Ulyah, S. M., Lin, X. C. S. and Miao, D. W. C. (2018). Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps. Finance Research Letters, 24, 113-128.Zhou, C., Wu, C. and Wang, Y. (2019). Dynamic portfolio allocation with time-varying jump risk. Journal of Empirical Finance, 50, 113-124.