PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY
PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY
摘要
In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.
基金
Project supported by the Yunnan Provincial Natural Science Foundation of China(No.00A0006R).
参考文献18
-
1Abramowitz, M. & Stegun, I. A., Handbook of mathematical functions with formulas, Graphs and Mathematical Tables, Dover, 1972.
-
2Barndorff-Nielsen, O. E., Normal inverse Gaussian processes and the modelling of stock returns, Research Report 300, Dept. Theor. Statistics, Aarhus University, 1995.
-
3Barndorff-Nielsen, O. E., Normal inverse Gaussian distributions and stochastic volatility modelling,Scand. J. Statist., 24(1997), 1-13.
-
4Barndorff-Nielsen, O. E., Processes of normal inverse Gaussian type, Finance and Stochastics, 2(1998),41-68.
-
5Barndorff-Nielsen, O. E., Jensen, J. L. & Sφrensen, M., Some stationry process in discrete and continuous type, Research Report 241, Dept. Theor. Statistics, Aarhus University, 1995.
-
6Barndorff-Nielsen, O. E. & Jiang, W., An initial analysis of some German stock price series, CAF working paper, No. 15, 1998.
-
7Barndorff-Nielsen, O. E. & Sφrensen, M., Asymptotic likelihood theory for stochastic processes, A review, Internat. Statist. Rev., 62(1994), 133-165.
-
8Bhattacharya, R. N., On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 60(1982), 185-201.
-
9Black, F. & Scholes, M., The pricing of options and corproate liabilities, Journal of Political Economy,81(1973), 673-659.
-
10Chesney, M. & Scott, L., Pricing European currency options: A comparison of the modified BlackScholes model and a random variance model, Journal of Financial and Quantitative Analysis, 24:3(1989),267-289.
-
1葛长有.服从某类分布证券的投资组合模型[J].集美大学学报（自然科学版）,2006,11(1):93-96.
-
2韩明,李月华,郝彦.证券投资的一种预测方法[J].统计与决策,2003,19(10):112-112. 被引量：3
-
3蒋文江,吴江强.一种QQ-Plot新生成方法及其在NIG分布中的应用（英文）[J].昆明理工大学学报（自然科学版）,2016,41(2):149-154.
-
4Xue Qiao DU Xu Guo YE.The Integration of Dual-Domain Method for Estimating the Volatility of Financial Assets[J].Journal of Mathematical Research and Exposition,2010,30(3):507-518.
-
5库热西.艾力尤甫,尼亚孜.苏来曼.证券组合的Markov链模型[J].经济数学,2001,18(3):42-46.
-
6戴丽霞.关于阶乘模p的序列Ⅱ(英文)[J].南京师大学报（自然科学版）,2008,31(4):33-36.
-
7ZHOU Xing-cai,HU Shu-he.Some Asymptotic Properties for Multivariate Partially Linear Models[J].Chinese Quarterly Journal of Mathematics,2011,26(2):270-274. 被引量：2
-
8Zhang Shihai,Zou Xianwu,Zhang Wenbin,Yuan Changying,Hu Jindong,Jin Zhunzhi,Peng Min.A System of Treatment for Correlation Signals[J].Wuhan University Journal of Natural Sciences,1998,3(3):50-54.
-
9王志刚.对数正态分布及其在证券中的应用[J].苏州市职业大学学报,2012,23(3):62-64.
-
10张若洵,杨世平.Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters[J].Chinese Physics B,2008,17(11):4073-4079. 被引量：1
