中国期权平价验证实验报告

实验二：期权平价关系在中国市场的实证检验

数据来源：武钢JTB1和武钢JTP1两只权证存续期为2005年11月23日到2006年11月22日，一共365天，为欧式，以股票交割结算。认沽权证执行价为K2=3.13元，认购执行价K1=2.9元，波动率为0.33，同期银行1年期的存款利率代替市场的无风险利率r=0.0225，武钢股票现价3.35元。一共选取了共计235对权证数据，在大智慧选取了日起对应的武钢股份数据。

（一）看跌权证价格调整

=-1.83

)=0.9451

Δ==0.22

Series P1=P-Δ

（二）回归模型的建立

Dependent Variable: CALL

Method: Least Squares

Date: 06/14/11 Time: 15:15

Sample: 1 235

Included observations: 235

Variable Coefficient Std. Error t-Statistic Prob.

P1 1.107950 0.058014 19.09796 0.0000

S 0.537330 0.033695 15.94685 0.0000

T 0.001921 0.000223 8.608702 0.0000

C -1.425408 0.113898 -12.51477 0.0000

R-squared 0.795055 Mean dependent var 0.812077

Adjusted R-squared 0.792394 S.D. dependent var 0.236382

S.E. of regression 0.107705 Akaike info criterion -1.601972

Sum squared resid 2.679670 Schwarz criterion -1.543086

Log likelihood 192.2317 F-statistic 298.7110

Durbin-Watson stat 0.248695 Prob(F-statistic) 0.000000

回归方程整体上比较好。但只有P的系数接近1，且常数项和股票价格S的回归系数都不显著。这显然和期权平价关系有很大出入。

ARCH模型

ARCH Test:

F-statistic 33.72762 Probability 0.000000

Obs*R-squared 71.31120 Probability 0.000000

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 06/14/11 Time: 15:22

Sample (adjusted): 4 235

Included observations: 232 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.004802 0.000942 5.098130 0.0000

RESID^2(-1) 0.326157 0.053311 6.118017 0.0000

RESID^2(-2) 0.069090 0.057405 1.203551 0.2300

RESID^2(-3) 0.074778 0.050201 1.489554 0.1377

R-squared 0.307376 Mean dependent var 0.009888

Adjusted R-squared 0.298262 S.D. dependent var 0.014180

S.E. of regression 0.011878 Akaike info criterion -6.011089

Sum squared resid 0.032170 Schwarz criterion -5.951663

Log likelihood 701.2864 F-statistic 33.72762

Durbin-Watson stat 1.278548 Prob(F-statistic) 0.000000 方程残差具有ARCH效应，考虑引入GRACH模型分析序列call、p以及s间的关系。

Dependent Variable: CALL

Method: ML - ARCH (Marquardt) - Normal distribution

Date: 06/14/11 Time: 15:26

Sample: 1 235

Included observations: 235

Convergence achieved after 51 iterations

Variance backcast: ON

GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1)

Coefficient Std. Error z-Statistic Prob.

P1 1.101393 0.012055 91.36749 0.0000

S 0.036647 0.003110 11.78208 0.0000

T 0.001121 2.50E-05 44.80590 0.0000

Variance Equation

C 1.88E-05 1.43E-05 1.311765 0.1896

RESID(-1)^2 0.785992 0.167289 4.698401 0.0000

GARCH(-1) 0.413655 0.078853 5.245925 0.0000

R-squared 0.495821 Mean dependent var 0.812077

Adjusted R-squared 0.484813 S.D. dependent var 0.236382

S.E. of regression 0.169667 Akaike info criterion -2.874783

Sum squared resid 6.592183 Schwarz criterion -2.786453

Log likelihood 343.7870 Durbin-Watson stat 0.136944

进行显著性检验z1=8.41 z2=30.96

二者数值都远大于2，这表明期权平价关系在中国权证市场不成立。