Parameters Estimations for Continuous-Time Stochastic Volatility Models
详细信息 查看官网全文
- 英文论文题名：Parameters Estimations for Continuous-Time Stochastic Volatility Models
- 论文作者：Ximei Wang ; Hang Zhang ; Yanlong Zhao
- 英文论文作者：Ximei Wang ; Hang Zhang ; Yanlong Zhao ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences
- 年：2017
- 作者机构：Academy of Mathematics and Systems Science,Chinese Academy of Sciences;
- 英文论文关键词：Stochastic Volatility model ; Parameters Estimation ; Maximum Likelihood Estimation ; It? Formula ; Mean-Reverting
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：F830.91
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：356k
- 原文格式：D
- 会议级别：全国
摘要
Stochastic volatility(SV) models take a very important role in financial market, while there still exist some difficulties in estimating parameters in SV models. In this paper, a unified parameter estimation algorithm is proposed to estimate continuoustime SV model. Parameters in equity prices and volatilities stochastic processes are estimated separately after orthogonalization of Brownian motion in SV models. A closed-form of Maximum Likelihood Estimation(MLE) and moment estimation results for four parameters in SV models are deducted. Five typical SV models are simulated to reveal the characteristics in empirical volatilities data. Parameter estimation results are presented to prove the convergence of estimation algorithm. We also compare our algorithm with Least Square(LS) estimations and numerical solutions of all the parameters in with MLE method, respectively.LS can only work in a specific form of SV models and the convergence speed is limited. Numerical solutions of the likelihood function with four parameters are unstable and can not converge to true values of all the parameters. Thus our algorithm works more efficiently than other methods.
Stochastic volatility(SV) models take a very important role in financial market, while there still exist some difficulties in estimating parameters in SV models. In this paper, a unified parameter estimation algorithm is proposed to estimate continuoustime SV model. Parameters in equity prices and volatilities stochastic processes are estimated separately after orthogonalization of Brownian motion in SV models. A closed-form of Maximum Likelihood Estimation(MLE) and moment estimation results for four parameters in SV models are deducted. Five typical SV models are simulated to reveal the characteristics in empirical volatilities data. Parameter estimation results are presented to prove the convergence of estimation algorithm. We also compare our algorithm with Least Square(LS) estimations and numerical solutions of all the parameters in with MLE method, respectively.LS can only work in a specific form of SV models and the convergence speed is limited. Numerical solutions of the likelihood function with four parameters are unstable and can not converge to true values of all the parameters. Thus our algorithm works more efficiently than other methods.
Stochastic volatility(SV) models take a very important role in financial market, while there still exist some difficulties in estimating parameters in SV models. In this paper, a unified parameter estimation algorithm is proposed to estimate continuoustime SV model. Parameters in equity prices and volatilities stochastic processes are estimated separately after orthogonalization of Brownian motion in SV models. A closed-form of Maximum Likelihood Estimation(MLE) and moment estimation results for four parameters in SV models are deducted. Five typical SV models are simulated to reveal the characteristics in empirical volatilities data. Parameter estimation results are presented to prove the convergence of estimation algorithm. We also compare our algorithm with Least Square(LS) estimations and numerical solutions of all the parameters in with MLE method, respectively.LS can only work in a specific form of SV models and the convergence speed is limited. Numerical solutions of the likelihood function with four parameters are unstable and can not converge to true values of all the parameters. Thus our algorithm works more efficiently than other methods.
引文
[1]A.L.Lewis,Option valuation under stochastic volatility:with mathematica code.Finance Press,2000.
[2]S.L.Heston,S.Nandi,A closed-form GARCH option valuation model.Review of Financial Studies,13(3):585-625,2000.
[3]S.L.Heston,A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.Review of Financial Studies,6(2):327-343,1993.
[4]S.L.Heston.A Simple New Formula for Options With Stochastic Volatility.Social Science Electronic Publishing,1997.
[5]R.Sch?bel,J.Zhu,Stochastic Volatility With an OrnsteinUhlenbeck Process:An Extension.European Finance Review,3(1):23-46,1998.
[6]E.M.Stein,J.C.Stein,Stock price distributions with stochastic volatility:an analytic approach.Review of financial Studies,4(4):727-752,1991.
[7]J.B.Wiggins,Option values under stochastic volatility:Theory and empirical estimates.Journal of Financial Economics,19(2):351-372,1987.
[8]J.Hull,A.White.The pricing of options on assets with stochastic volatilities.The Journal of Finance,42(2):281-300,1987.
[9]F.Black,M.Scholes.The pricing of options and corporate liabilities.Journal of Political Economy,81(3):637-654,1973.
[10]A.R.Gallant,G.Tauchen.Which Moments to Match?,Econometric Theory,12(4):657-681,1996.
[11]S.Taylor,Modeling Financial Time Series.Economic Journal,97(386),1987.
[12]R.F.Engle,Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.Econometrica,50(4):987-1007,1982.
[13]J.C.Cox,J.E.I.Jr,S.A.Ross,A Theory of the Term Structure of Interest Rates.Theory Of Valuation.129-164,2014.
[14]O.Vasicek.An equilibrium characterization of the term structure,Journal of Financial and Quantitative Analysis,5(4):177-188,1977.
1 see Appendix for orthogonalize the noise of volatility process.
[2]S.L.Heston,S.Nandi,A closed-form GARCH option valuation model.Review of Financial Studies,13(3):585-625,2000.
[3]S.L.Heston,A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.Review of Financial Studies,6(2):327-343,1993.
[4]S.L.Heston.A Simple New Formula for Options With Stochastic Volatility.Social Science Electronic Publishing,1997.
[5]R.Sch?bel,J.Zhu,Stochastic Volatility With an OrnsteinUhlenbeck Process:An Extension.European Finance Review,3(1):23-46,1998.
[6]E.M.Stein,J.C.Stein,Stock price distributions with stochastic volatility:an analytic approach.Review of financial Studies,4(4):727-752,1991.
[7]J.B.Wiggins,Option values under stochastic volatility:Theory and empirical estimates.Journal of Financial Economics,19(2):351-372,1987.
[8]J.Hull,A.White.The pricing of options on assets with stochastic volatilities.The Journal of Finance,42(2):281-300,1987.
[9]F.Black,M.Scholes.The pricing of options and corporate liabilities.Journal of Political Economy,81(3):637-654,1973.
[10]A.R.Gallant,G.Tauchen.Which Moments to Match?,Econometric Theory,12(4):657-681,1996.
[11]S.Taylor,Modeling Financial Time Series.Economic Journal,97(386),1987.
[12]R.F.Engle,Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.Econometrica,50(4):987-1007,1982.
[13]J.C.Cox,J.E.I.Jr,S.A.Ross,A Theory of the Term Structure of Interest Rates.Theory Of Valuation.129-164,2014.
[14]O.Vasicek.An equilibrium characterization of the term structure,Journal of Financial and Quantitative Analysis,5(4):177-188,1977.
1 see Appendix for orthogonalize the noise of volatility process.