臺灣博碩士論文加值系統

本研究使用標準普爾500指數收益率，從1996年1月到2016年12月。資產價格過程遵循GARCH-Jump模型，跳躍成分被假設為正態高斯逆分佈（NIG）。 我們利用粒子濾波方法估計模型參數，然後分別計算模型隱含總方差（MTV），模型隱含正態方差（MNV）和模型隱含跳變方差（MJV）。 我們發現，只有MTV和MNV的預測值分別為4個月到12個月。 MJV陽性預測12個月是顯著的。 在MNV和MJV聯合後，MNV與未來4個月至12個月的市場收益呈顯著正相關。 我們的結論是，預測總變差的能力發生在跳躍部分。

This study uses S&P 500 index returns from January 1996 to December 2016. The asset price process follows GARCH-Jump model and the jump component is pretended to be normal inverse Gaussian (NIG) distribution. We make use of the particle filter method to estimate the parameters of our model and then calculate the model-implied total variance (MTV), model-implied normal variance (MNV), and model-implied jump variance (MJV), respectively. We find that there is positive significantly prediction from four months to twelve months with MTV only, and MNV only, respectively. MJV positive predictions for 12 months were significant. After MNV and MJV jointly, MNV has positive significantly relation with future market returns from four months to twelve months. Our conclusion is that the ability to predict total variation occurs in the jump part.

1 Introduction---------------------------------------------------------------------------p.1
2 Model---------------------------------------------------------------------------------p.3
3 Data and Estimation-------------------------------------------------------------------p.4
3.1 Data---------------------------------------------------------------------------------p.4
3.2 Particle Filter-------------------------------------------------------------------------p.4
3.3 Estimation---------------------------------------------------------------------------p.6
4 Empirical analysis----------------------------------------------------------------------p.7
4.1 Variable Definition--------------------------------------------------------------------p.7
4.2 Descriptive statistics for estimated variable-------------------------------------------p.7
4.3 Results------------------------------------------------------------------------------p.8
5 Conclusion----------------------------------------------------------------------------p.9 * Reference-----------------------------------------------------------------------------p.11

References
1.Abel, A.B., 1988. Stock Price Under Time-Varying Dividend Risk: An Exact Solution in an Infinite-Horizon General Equilibrium Model. Journal of Monetary Economics 22, 375-393.
2.Amihud, Y., 2002. Illiquidity and Stock Returns: Cross-Section and Time-Series Effects. Journal of Financial Markets 5, 31-56.
3.Barndorff-Nielsen, O.E. and N. Shephard, 2000. Econometric Analysis of Realised Volatility and its Use in Estimating Levy Based Non-Gaussian OU Type Stochastic Volatility Models. Manuscript, Nuffield College, Oxford, United Kingdom.
4.Bégin, J.-F., C. Dorion, and G. Gauthier, 2018. Idiosyncratic jump risk matters: evidence from equity returns and options. Working Paper, HEC Montéal.
5.Bollerslev, T., G. Tauchen, H. Zhou, 2009. Expected stock returns and variance risk premia. Review of Financial Studies 22, 4463-4492.
6.Bollerslev, Tim, Robert Engle and J.M. Wooldridge, 1988. A Capital Asset Pricing Model with Time Varying Covariances. Journal of Political Economy 96, 116-131.
7.Bollerslev, T., Todorov, V., and Xu, L, 2015. Tail risk premia and return predictability. Journal of Financial Economics 118, 113-134.
8.Carr, P., H. Geman, D. Madan, M. Yor, 2002. The fine structure of asset returns: an empirical investigate. Journal of Business 75, 305-332.
9.Christoffersen, P., S. Heston, and K. Jacobs, 2013. Capturing Option Anomalies with a Variance-Dependent Pricing Kernel. The Review of Financial Studies 26, 1963-2006.
10.Duffie, D., Pan, J., Singleton, K., 2000. Transform analysis and asset pricing for affine
jump-diffusions. Econometrical 68, 1343-1376. 11
11.Fama, E. and K. French, 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics 33, 3-56.
12.French, K. R., Schwert, G., & Stambaugh, R. F., 1987. "Expected Stock Returns and Volatility, " Journal of Financial Economics 19, 3-29.
13.Gordon, N.J., D.J. Salmond and A.F.M. Smith,1993. "A novel approach to nonlinear/non-Gaussian Bayesian state estimation, " In: IEE Proceedings on Radar and Signal Processing. Vol. 140, 107-113.
14.Heston, S., 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud 6, 327-343.
15.Malik, S., and M. K. Pitt, 2011. Particle Filters for Continuous Likelihood Evaluation and Maximisation. Journal of Econometrics 165,190-209.
16.Merton, R.C., 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation, " Journal of Financial Economics 8, 323-361.
17.Ornthanalai, C., 2014. Lévy jump risk: Evidence from options and returns. Journal of Financial Economics 112, 69-90.
18.Pindyck,Robert S., 1981. Risk, inflation, and the stock market. American Economic Review 714, 335-351.
19.Poterba, James and Lawrence Summers, 1988. Mean Reversion in Stock Prices: Evidence and Implications. Journal of Financial Economics 27-60.