中国股票认股权证的定价研究
摘要
本文在回顾中国股票认股权证发展历程及分析目前国内认股权证市场机制和价格特征的基础上,通过着重考虑随机波动率的定价模型,对认股权证进行了系统的定价研究。具体来说,本文在用目前常用的众多波动率模型——随机游走模型、GARCH族模型、跳跃模型及残差非正态分布模型对股票收益率数据进行拟合的基础上,利用Hong&Li(2005)非参数模型设定检验方法,比较各个模型的设定误差,寻找出模型设定误差最小的模型是含跳跃因子的GARCH族模型和残差非正态分布模型。然后,在掌握标的股票价格波动率特征的基础上,利用蒙特卡罗模拟技术对股价路径进行模拟,从而对权证进行合理定价。之后再结合我国特殊的制度背景,做出定价结果分析及敏感性分析,得出含跳跃因子的GARCH模型最适合作为我国权证的定价基准。最后,为了完善权证市场的定价机制,本文提出建立全面套利机制和发展真正期权市场等政策建议。
This paper did a systematic research on the price of Chinese Warrant after the reform of stock market. Having analyzed the history and mechanism of Warrant Market in China and special view on the wholly theory of warrant pricing, and focus on the aspect of stochastic process as well, this paper used a lot of popular volatility models, such as Random Walking Model, GARCH Models, Models with Jump factors and non-normal Models to study the dynamic behavior of underlying stocks and then used Hong & Lee (2005) nonparametric specification test to compare the model specification errors of different models. Based on the result of volatility estimation, the writer used the Monte-Carlo simulations to price the warrants and compare the pricing results of different models. The pricing results showed that the Warrants in Chinese market are seriously overpriced nowadays. There is also a strong manipulation in the market. The writer studied some possible institutional reasons for such manipulation and proposed some policy suggestions in the end.
This paper did a systematic research on the price of Chinese Warrant after the reform of stock market. Having analyzed the history and mechanism of Warrant Market in China and special view on the wholly theory of warrant pricing, and focus on the aspect of stochastic process as well, this paper used a lot of popular volatility models, such as Random Walking Model, GARCH Models, Models with Jump factors and non-normal Models to study the dynamic behavior of underlying stocks and then used Hong & Lee (2005) nonparametric specification test to compare the model specification errors of different models. Based on the result of volatility estimation, the writer used the Monte-Carlo simulations to price the warrants and compare the pricing results of different models. The pricing results showed that the Warrants in Chinese market are seriously overpriced nowadays. There is also a strong manipulation in the market. The writer studied some possible institutional reasons for such manipulation and proposed some policy suggestions in the end.
引文
1 见Jackwerth and Rubinstein(1996)。
2 见上交所创新实验室研究报告“创设机制与我国权证市场定价效率研究”,上海证券报,2006.09.08。
3 刘岱“沪深权证市场统计分析报告(2005年8月—2006年8月)”,银河证券研究中心,2006.08.31。
4 见郑振龙主编的《金融工程》第十章套期保值行为。
5 参见H.E.Leland,"Option pricing and replication with transaction costs",Journal of Finance,1985,40:1283-1301.
6 更详细的推导和分析参见T.Hoggard,A.E.Whalley and P.Wilmott,"Hedging option portfolios in the presence of transaction costs".Advances in Futures and Options Research,1994,7:21-35.
[1]Black,F.and Scholes,M..The pricing of option and corporation liabilities[J].Journal of Political Economy,1973,81:637-659.
[2]Hayne,E.Leland.Option Pricing and Replication with Transactions Costs[J].The Journal of Finance,1985,5:1283-1301.
[3]Whalley,A.E.and Wiimott P..Asymptotic Analysis of an optimal hedging model[J].Mathematical Finance,1997,7(3):307-324.
[4]Melton,R.C..Option Pricing when Underlying Stock Returns are Discontinuous[J].Journal of Financial Economics,1976,3:125-144.
[5]Cox,J.C.and S.A.Ross(1976b).The valuation of options for alternative stochastic processes[J].Journal of Financial Economics,1976,3:145-166.
[6]Cox,J.C.and M.Rubinstein.options Markets[M].Prentice-Hall,Englewood Cliffs,New Jersey,1985.
[7]Bernard Dumas,Jeff Fleming & Robert E.Whaley.Implied Volatility Functions:Empirical Tests[J].Journal of Finance,1998,53(6):2059-2106.
[8]Heston,S.L..A dosed-form solution for options with stochastic volatility with applications to bond and currency options[J].Review of Financial Studies,1993,6:327-344.
[9]Cao,C..Pricing foreign currency options with stochastic volatility.University of Chicago working paper,1992.
[10]Myers,R.J.and S.D.Hanson.Pricing commodity options when the underlying futures price exhibits time-varying volatility[J].American Journal of Agricultural Economics,1993,75:121-130.
[11]Amin,K.I.and V.K.Ng.ARCH processes and option valuation.University of Michigan working paper,1993.
[12]Duan,J.C..The GARCH option pricing model[J].Mathematical Finance,1995,5:13-32.
[13]Hull,J.and A.White.The pricing of options on assets with stochastic volatility[J].Journal of Finance,1987,42:281-300.
[14]Scott,L.O..Option pricing when the variance changes randomly:theory,estimation,and an application[J].Journal of Financial and Quantitative Analysis,1987,22:419-438.
[15]Johnson,H.and D.Shanno.Option pricing when the variance is changing[J].Journal of Financial and Quantitative Analysis,1987,22:143-151.
[16]Wiggins,J.B..Option values under stochastic volatility:theory and empirical estimates[J].Journal of Financial Economics,1987,19:351-377.
[17]Heston,S.L..A closed-form solution for options with stochastic volatility with applications to bond and currency options[J].Review of Financial Studies,1993,6:327-344.
[18]Galai,D.and Schneller,M.I.,.Pricing of warrants and the value of the firm[J].The Journal of Finance,1978:1333-1342.
[19]Schulz,G.U.and Trautmann,S..Robustness of option-like warrant valuation[J].Journal of Banking and Finance,1994:841-859.
[20]周延.认股权证的定价模型及其应用[J].预测,1998,17(5):56-58.
[21]唐国正等.期权,认股权证与可转换债券的定价[J].投资与合作,1998,12:29-33.
[22]王志成,何树红.认股权证的定价因素[J].华东经济管理,2002,16(3):118-120.
[23]Engle,R.E.Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation[J].Econometrica,1982,50:987-1007.
[24]Bollerslev T..Generalised autoregressive conditional eteroskedasticy[J].Journal of Econometrics,1986,31:307-327.
[25]Engle,R.F.,Lilien,D.M.and R.P.Robins.Estimating time-varying premia in the term structure:the ARCH-M model[J].Econometrica,1987,55:391-407.
[26]Nelson,D.B..Conditional Heteroskedasticity in Asset Retums:A New Approach[J].Econometrica,1991,59:347-370
[27]Zakoian,J.M..Threshold Heteroscedastic Models[J].Journal of Economic Dynamics and Control,1994,18:931-955.
[28]Lawrence R.Glosten,Ravi Jagannathan,David E.Runkle.On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks[J].The Journal of Finance,1993,48(5):1779-1801.
[29]岳朝龙.上海股市收益率GARCH模型族的实证研究[J].数量经济技术经济研究,2001,6:126-129.
[30]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002,263(5):67-73.
[31]俞乔.市场有效、周期异常与股价波动—对上海、深圳股票市场的实证分析[J].经济研究,1994,9:43-50.
[32]田新时,刘汉中,李耀.沪深股市一般误差分布(GED)下的VaR计算[J].管理工程学报,2003.1:25-28.
[33]French K.R.,Schwert G.W.,Stambaugh R..Expected Stock Return and Volatility[J].Journal of Financial Economics,1987,19:3-29.
[34]吴其明,季忠贤,杨晓荣.自回归条件异方差(ARCH)模型及应用[J].预测,1998,17(4):47-54.
[35]王安兴,孙琼,林少宫.中国外汇市场波动分析[J].统计研究,1998,1:25-29.[36]吴长凤.利用回归-GARCH模型对我国沪深股市的分析[J].预测,1999,4:46-47.
[37]张思奇,马刚,冉华.股票市场风险、收益与市场效率-ARMA-ARCH-M模型[J].世界经济,2000,5:19-28.
[38]郑振龙.金融工程[M].高等教育出版社,2003.
2 见上交所创新实验室研究报告“创设机制与我国权证市场定价效率研究”,上海证券报,2006.09.08。
3 刘岱“沪深权证市场统计分析报告(2005年8月—2006年8月)”,银河证券研究中心,2006.08.31。
4 见郑振龙主编的《金融工程》第十章套期保值行为。
5 参见H.E.Leland,"Option pricing and replication with transaction costs",Journal of Finance,1985,40:1283-1301.
6 更详细的推导和分析参见T.Hoggard,A.E.Whalley and P.Wilmott,"Hedging option portfolios in the presence of transaction costs".Advances in Futures and Options Research,1994,7:21-35.
[1]Black,F.and Scholes,M..The pricing of option and corporation liabilities[J].Journal of Political Economy,1973,81:637-659.
[2]Hayne,E.Leland.Option Pricing and Replication with Transactions Costs[J].The Journal of Finance,1985,5:1283-1301.
[3]Whalley,A.E.and Wiimott P..Asymptotic Analysis of an optimal hedging model[J].Mathematical Finance,1997,7(3):307-324.
[4]Melton,R.C..Option Pricing when Underlying Stock Returns are Discontinuous[J].Journal of Financial Economics,1976,3:125-144.
[5]Cox,J.C.and S.A.Ross(1976b).The valuation of options for alternative stochastic processes[J].Journal of Financial Economics,1976,3:145-166.
[6]Cox,J.C.and M.Rubinstein.options Markets[M].Prentice-Hall,Englewood Cliffs,New Jersey,1985.
[7]Bernard Dumas,Jeff Fleming & Robert E.Whaley.Implied Volatility Functions:Empirical Tests[J].Journal of Finance,1998,53(6):2059-2106.
[8]Heston,S.L..A dosed-form solution for options with stochastic volatility with applications to bond and currency options[J].Review of Financial Studies,1993,6:327-344.
[9]Cao,C..Pricing foreign currency options with stochastic volatility.University of Chicago working paper,1992.
[10]Myers,R.J.and S.D.Hanson.Pricing commodity options when the underlying futures price exhibits time-varying volatility[J].American Journal of Agricultural Economics,1993,75:121-130.
[11]Amin,K.I.and V.K.Ng.ARCH processes and option valuation.University of Michigan working paper,1993.
[12]Duan,J.C..The GARCH option pricing model[J].Mathematical Finance,1995,5:13-32.
[13]Hull,J.and A.White.The pricing of options on assets with stochastic volatility[J].Journal of Finance,1987,42:281-300.
[14]Scott,L.O..Option pricing when the variance changes randomly:theory,estimation,and an application[J].Journal of Financial and Quantitative Analysis,1987,22:419-438.
[15]Johnson,H.and D.Shanno.Option pricing when the variance is changing[J].Journal of Financial and Quantitative Analysis,1987,22:143-151.
[16]Wiggins,J.B..Option values under stochastic volatility:theory and empirical estimates[J].Journal of Financial Economics,1987,19:351-377.
[17]Heston,S.L..A closed-form solution for options with stochastic volatility with applications to bond and currency options[J].Review of Financial Studies,1993,6:327-344.
[18]Galai,D.and Schneller,M.I.,.Pricing of warrants and the value of the firm[J].The Journal of Finance,1978:1333-1342.
[19]Schulz,G.U.and Trautmann,S..Robustness of option-like warrant valuation[J].Journal of Banking and Finance,1994:841-859.
[20]周延.认股权证的定价模型及其应用[J].预测,1998,17(5):56-58.
[21]唐国正等.期权,认股权证与可转换债券的定价[J].投资与合作,1998,12:29-33.
[22]王志成,何树红.认股权证的定价因素[J].华东经济管理,2002,16(3):118-120.
[23]Engle,R.E.Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation[J].Econometrica,1982,50:987-1007.
[24]Bollerslev T..Generalised autoregressive conditional eteroskedasticy[J].Journal of Econometrics,1986,31:307-327.
[25]Engle,R.F.,Lilien,D.M.and R.P.Robins.Estimating time-varying premia in the term structure:the ARCH-M model[J].Econometrica,1987,55:391-407.
[26]Nelson,D.B..Conditional Heteroskedasticity in Asset Retums:A New Approach[J].Econometrica,1991,59:347-370
[27]Zakoian,J.M..Threshold Heteroscedastic Models[J].Journal of Economic Dynamics and Control,1994,18:931-955.
[28]Lawrence R.Glosten,Ravi Jagannathan,David E.Runkle.On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks[J].The Journal of Finance,1993,48(5):1779-1801.
[29]岳朝龙.上海股市收益率GARCH模型族的实证研究[J].数量经济技术经济研究,2001,6:126-129.
[30]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002,263(5):67-73.
[31]俞乔.市场有效、周期异常与股价波动—对上海、深圳股票市场的实证分析[J].经济研究,1994,9:43-50.
[32]田新时,刘汉中,李耀.沪深股市一般误差分布(GED)下的VaR计算[J].管理工程学报,2003.1:25-28.
[33]French K.R.,Schwert G.W.,Stambaugh R..Expected Stock Return and Volatility[J].Journal of Financial Economics,1987,19:3-29.
[34]吴其明,季忠贤,杨晓荣.自回归条件异方差(ARCH)模型及应用[J].预测,1998,17(4):47-54.
[35]王安兴,孙琼,林少宫.中国外汇市场波动分析[J].统计研究,1998,1:25-29.[36]吴长凤.利用回归-GARCH模型对我国沪深股市的分析[J].预测,1999,4:46-47.
[37]张思奇,马刚,冉华.股票市场风险、收益与市场效率-ARMA-ARCH-M模型[J].世界经济,2000,5:19-28.
[38]郑振龙.金融工程[M].高等教育出版社,2003.