金融工程中资产收益的连续时间模型评述

摘要/Abstract

摘要： 总结了在过去30年中金融资产收益连续时间模型的发展及主要成果,讨论了迄今连续时间模型参数估计的主要方法,其中特别讨论了MCMC方法;最后指出了现在和未来该领域研究所面临的主要课题。

关键词: 连续时间模型, 跳跃-扩散模型, 马尔可夫链蒙特卡罗方法, 资产收益, 波动

Abstract: Firstly,this paper surveys and assesses the development and main fruits of continuous-time equity return models during the last 30 years.Then it discusses the estimation methods of these models,and mainly studies the McMC method.In the end,we also point out the new areas of future research along these lines.

Key words: continue-time models, jump-diffusion models, markov chain monte carlo method, equity return, volatility

中图分类号:

C934

胡素华, 张世英, 张彤. 金融工程中资产收益的连续时间模型评述[J]. 中国管理科学, 2006, (2): 24-32.

HU Su-hua, ZHANG Shi-ying, ZHANG Tong. Review on Continuous-Time Equity Return Models in Financial Engineering[J]. Chinese Journal of Management Science, 2006, (2): 24-32.

参考文献

[1] Merton,Robert C.Lifetime portfolio selection under uncertainty:The continuous time case[J].Review of Economics and Statistics,1969,51:247-257.
[2] Scott,Louis.Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates:Applications of Fourier inversion methods[J].Mathematical Finance,1997,7:413-426.
[3] 杨智元,陈浪南.基于跳跃过程的指数期权模型[J].经济研究,2001,2:61-66.
[4] Hull,John,and Alan White.The impact of default risk on the prices of options and other derivative securities[J].Journal of Banking and Finance,1995,19:299-322.
[5] 郭磊,吴冲锋.基于价值分解的CAPM"异常现象"理论解释[J].中国管理科学,2005,13(1):14-18.
[6] Hull,John C.and Alan White.The pricing interest rate caps and floors using the Hull-White model[J].Journal of Financial Engineering,1994,(2):287-296.
[7] Campbell,John Y.,and Luis Viceira.Consumption and portfolio decisions when expected returns are time varying[J].Quarterly Journal of Economics,1999,114:433-495.
[8] 郭文旌.跳跃扩散股价的最优股资组合选择[J].控制理论与应用,2005,(2):171-176.
[9] Black,F.and Scholes,M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973,81:637-659.
[10] S.G.Kou.A jump-diffusion model for option pricing[J].Management Science,2002,48(8):1086-1101.
[11] 沈根祥.股票收益随机波动模型研究[J].中国管理科学,2003,11(2):16-19.
[12] Merton,Robert C.Theory of Rational Option Pricing[J].Bell Journal of Economics,1973,4:141-183.
[13] Cox,J.C.and S.Ross.The Valuation of Options for Alternative Stochastic Processes[J].Journal of Financial Economics,1976,3:145-166.
[14] Merton,Robert C.Option Pricing when Underlying Stock Returns Are Discontinuous[J].Journal of Financial Economics,1976,3:125-144.
[15] Cox,John C.,Jonathan E.Ingersoll,Jr.,and Stephen A.Ross.A Theory of the Term Structure of Interest Rates[J].Econometrica,1985,53:385-407.
[16] Hull,J.C.and White,A.The pricing of options on assets with stochastic volatilities[J].Journal of Finance,1987,42:281-300.
[17] Heston,Steven L.A Closed Form Solution for Optiono with Stochastic Volatility with Applications to Bond and Currency Options[J].The Review of Financial Studies,1993,6:327-343.
[18] Bates,D.S.Jumps and Stochastic Volatility:Exchange Rate Processes Implicit in Deutsche Mark Options[J].The Review of Financial Studies,1996,9:69-107.
[19] Andersen,T.G,L.Benzoni,and J.Lund.An Empirical Investigation of Continuous Time Models for Equity Returns[J].Journal of Finance,2002,57 (3):1239-1284.
[20] Duffie,D.,Jun Pan,and K.J.Singleton.Transform Analysis and Asset Pricing for Affine Jump-Diffusions[J].Econometrica,2000,68:1343-1376.
[21] Eraker,B.,M.J.Johannes,and N.G.Polson.The Impact of Jumps in Returns and Volatility[J].Journal of Finance,2003,53(3):1269-1300.
[22] Eraker,B.Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices[J].Journal of Finance,2004,59(3):1367-1404.
[23] Cox,J.C.The Constant Elasticity of Variance Option Pricing Model[J].The Journal of Portfolio Management,1996,2:15-17.
[24] Melino Angelo,and Stuart M.Turnbull.Pricing Foreign currency Options with Stochastic Volatility[J].Journal of Econometrics,1990,45:239-265.
[25] Benzoni,L.Pricing Options under Stochastic Volatility:an Econometric Analysis[Z].Working Paper,University of Minnesota,1998.
[26] Eberlein,E.and Keller,U.Hyperbolic distributions in finance[J].Bernoulli,1995,1:281-299.
[27] Barndorff-Nielsen,O.E.and Shephard,N.Modeling by Levy processes for financial econometrics[C],in O.E.Barndorff-Nielsen,T.Mikosch and S.I.Resnick (eds),Levy Processes-Theory and Applications,BirkhAauser,Basel,2001:283-318.
[28] Schoutens,W.Levy Processes in Finance-Pricing Financial Derivatives[M].Wiley Series in Probability and Statistics.John Wiley and Sons,Chichester,2003.
[29] Barndorff-Nielsen,O.E.and Shephard,N.Continuous Time Approach to Financial Volatility[M].Cambridge Vniversity Press.2005,To appear.
[30] Rydberg,T.H.The normal inverse Gaussian Levy process:Simulation and approximation[J].Communication in Statistics:Stochastic Models,1997,13:887-910.
[31] B.M.Bibby and M.Sorensen.A hyperbolic diffusion model for stock prices[J].Finance and Stochastic,1997,(1):25-41.
[32] T.H.Rydberg.Generalized hyperbolic diffusion processes with applications in finance[J].Mathematical Finance,1999,9(2):183-201.
[33] Cont,R.and Tankov,P.Financial Modeling with Jump Processes[M].Chapman & Hall/CRC,London,2004.
[34] Emmer,S.amd KlAuppelberg,C.Optimal portfolios when stock prices follow an exponential Levy process[J].Finance and Stochastics,2004,8:17-44.
[35] 胡素华,张世英,张彤.资产价格的抛物线跳跃扩散模型[J].系统工程理论与实践,2006.待刊.
[36] Lo,Andrew.Maximum likelihood estimation of generalized Ito processes with discretely sampled data[J].Econometric Theory,1988,4:231-47.
[37] Ait-Sahalia,Y.Nonparametric pricing of interest rate derivative securities[J].Econometrica,1996,64:527 -560.
[38] Gallant,A.Ronald,and George Tauchen.Which Moments to Match?[J].Econometric Theory,1996,(12):657-681.
[39] Duffie,Darrell,and Kenneth J.Singleton.Simulated Moments Estimation of Markov Models of Asset Prices[J].Econometrica,1993,61:929-952.
[40] Pedersen Asger.A New Approach to Maximum Likelihood Estimation for Stochastic Differential Equations Based on Discrete Observations[J].Scandinavian Journal of Statistics,1995,22 (1):55-71.
[41] Eraker,Bjorn.MCMC Analysis of Diffusion Models with Application to Finance[J].Journal of Business and Eeonomic Statistics,2001,19:177-191.
[42] Jones,Christopher S.Bayesian Estimation of ContinuousTime Finance Models[Z].Working Paper,Rochester University,1998.
[43] Elerian,Ola,Siddhartha Chib,and Neil Shephard.Likelihood Inference for Discretely Observed Non-linear Diffusions[J].Econometrica,2001,69:959-993.
[44] Y K Tse、Xibin Zhang and Jun Yu.Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method[J].Quantitative Finance,2003,3 (1):1-12.
[45] 胡素华,张彤,张世英.NIG扩散模型的McMC估计[J].系统过程理论方法应用,2006.待刊.
[46] Elerian O.A note on the existence of a closed-form conditional transition density for the Milstein scheme[Z].Eeonomics Discussion Paper,1998-W18 Nuffield College,Oxford
[47] Chibs S and Greenberg E.Understanding the MetropolisHastings algorithm[J].American Statistician,1995,49:327-35.
[48] Roberts G O.Markov chain concepts related to sampling algorithms[C].Markov Chain Monte Carlo in Practice,ed W R Gilks,S Richardson and D J Spiegelhalter(London:Chapman and Hall),1996:45-57.
[49] Kim S,Shephard N and Chibs.Stochastic volatility:likelihood inference and comparison with ARCH models[J].Review of Economic Studies,1998,65(2):361-93.
[50] Meyer R and J Yu.BUGS for a Bayesian analysis of stochastic volatility models[J].Econometrics Journal,2000,3(2):198-215.