[1]崔海蓉,胡小平.基于GMD的隐含最小距离风险中性概率测度提取[J].东南大学学报(自然科学版),2011,41(1):210-214.[doi:10.3969/j.issn.1001-0505.2011.01.041]
 Cui Hairong,Hu Xiaoping.Recovering implied minimum distance risk-neutral probability measure using GMD[J].Journal of Southeast University (Natural Science Edition),2011,41(1):210-214.[doi:10.3969/j.issn.1001-0505.2011.01.041]
点击复制

基于GMD的隐含最小距离风险中性概率测度提取()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
41
期数:
2011年第1期
页码:
210-214
栏目:
经济与管理
出版日期:
2011-01-20

文章信息/Info

Title:
Recovering implied minimum distance risk-neutral probability measure using GMD
作者:
崔海蓉胡小平
(东南大学经济管理学院, 南京 211189)
Author(s):
Cui HairongHu Xiaoping
(School of Economics and Management, Southeast University, Nanjing 211189, China)
关键词:
风险中性概率测度高斯混合分布最小距离
Keywords:
risk-neutral probability measure Gaussian mixture distributions minimum distance
分类号:
F830.9
DOI:
10.3969/j.issn.1001-0505.2011.01.041
摘要:
提出了一种从期权价格恢复标的资产隐含风险中性概率测度的新方法.在不完全市场条件下,运用高斯混合分布(GMD)构建了恢复最小距离隐含风险中性概率测度的数学优化模型,并进一步讨论模型的求解方法与技巧.采用欧式期权数据,通过数值实验对模型的有效性进行验证.实验结果表明,实际风险中性概率测度可由2个组成部分的高斯混合分布近似,形状更加具有尖峰性,且是双峰,左尾处含有一个较小峰值.这说明市场参与者对未来的预期集中度比较高,但市场对极端不利价格运动的预期(左尾部)比极端有利价格运动(右尾部)的预期要高,因此传统标的资产价格对数正态分布的假设会低估损失发生的可能性.
Abstract:
A new approach to estimate the implied risk-neutral probability measure of the underlying assets from option prices is presented. Under incomplete market conditions, Gaussian mixture distribution (GMD) was used to construct the mathematical optimization model of restoring the minimum distance implied risk-neutral probability measure. Furthermore, solving methods and techniques of the optimization model were discussed. The effectiveness of the model was tested using European option data. The results show that the real risk-neutral probability measure can be approximated by the Gaussian mixture distribution of two components; the shape of it is more leptokurtic, being bimodal with a smaller peak at the left tail. This indicates that market participants expect the future with higher concentration. However, expectation for extremely unfavorable price movement (left tail) is higher than that for the extremely favorable price movement (right tail), so traditional assumptions on the underlying asset with lognormal distribution would underestimate potential loss.

参考文献/References:

[1] Flamouris D,Giamouridis D.Estimating implied PDFs from American options on futures:a new semiparametric approach[J].Journal of Futures Markets,2002,22(1):1-30.
[2] Bondarenko O.Estimation of risk-neutral densities using positive convolution approximation[J].Journal of Econometrics,2003,116(2):85-112.
[3] Jackwerth J C.Option-implied risk-neutral distributions and implied binomial trees[J].Journal of Derivatives,1999,7(2):66-82.
[4] Breeden D T,Litzenberger R H.Prices of state-contingent claims implicit in option prices[J].Journal of Business,1978,51(4):621-651.
[5] Haven E,Liu X,Ma C,et al.Revealing the implied risk-neutral MGF from options:the wavelet method[J].Journal of Economic Dynamics and Control,2009,33(3):692-709.
[6] Shimko D.Bounds of probability[J].Risk,1993,6(4):33-37.
[7] Malz A M.Estimating the probability distribution of the future exchange rate from option prices[J].The Journal of Derivatives,1997,5(2):18-36.
[8] Bates D S.The crash of ’87:was it expected? the evidence from options markets[J].Journal of Finance,1991,46(3):1009-1044.
[9] Bliss R R,Panigirtzoglou N.Testing the stability of implied probability density functions[J].Journal of Banking and Finance,2002,26(2/3):381-422.
[10] 周娟,韩立岩.基于外汇期货期权的隐含风险中性概率的复原与市场情绪[J].系统工程理论与实践,2008,28(8):197-205.
  Zhou Juan,Han Liyan.Recovering of implied risk-neutral probability distributions of foreign exchange futures options and market sentiment [J].Systems Engineering—Theory &Practice,2008,28(8):197-205.(in Chinese)
[11] Melick W R,Thomas C P.Recovering an asset’s implied PDF from option prices:an application to crude oil during the Gulf crisis[J].Journal of Financial and Quantitative Analysis,2009,32(1):91-115.
[12] Fabozzi F J,Tunaru R,Albota G.Estimating risk-neutral density with parametric models in interest rate markets[J].Quantitative Finance,2009,9(1):55-70.
[13] Rubinstein M.Implied binomial trees[J].Journal of Finance,1994,49(3):771-818.
[14] Ait-Saholia Y,Lo A.Nonparametric estimation of state-price densities implicit in financial asset prices[J].Journal of Finance,1998,53(2):499-547.
[15] Hutchinson J M,Lo A W,Poggio T.A nonparametric approach to pricing and hedging derivative securities via learning networks[J].Journal of Finance,1994,49(3):851-889.
[16] Garcia R,Gencay R.Pricing and hedging derivative securities with neural networks and a homogeneity hint[J].Journal of Econometrics,2000,94(1):93-115.
[17] Gencay R,Gibson R.Model risk for European-style stock index options[J].IEEE Transactions on Neural Networks,2007,18(1):193-202.
[18] Rompolis L S.Retrieving risk neutral densities from European option prices based on the principle of maximum entropy[J].Journal of Empirical Finance,2010,17(5):918-937.
[19] Abadir K M,Rockinger M.Density functionals,with an option-pricing application[J].Econometric Theory,2003,19(5):778-811.
[20] Bondarenko O.Estimation of risk-neutral densities using positive convolution approximation[J].Journal of Econometrics,2003,116(2):85-112.
[21] Monteiro A M,Tütüncü R H,Vicente L N.Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity[J].European Journal of Operational Research,2008,187(2):525-542.
[22] Hull J,White A.Value at risk when daily changes in market variables are not normally distributed[J].The Journal of Derivatives,1998,5(3):9-19.
[23] Venkataraman S.Value at risk for a mixture of normal distributions:the use of quasi-bayesian estimation techniques[J].Economic Perspectives,1997,21(2):45-56.
[24] Ané T,Labidi C.Revisiting the finite mixture of Gaussian distributions with application to futures markets[J].Journal of Futures Markets,2001,21(4):347-376.
[25] Buckley I,Saunders D,Seco L.Portfolio optimization when asset returns have the Gaussian mixture distribution[J].European Journal of Operational Research,2008,185(3):1434-1461.

备注/Memo

备注/Memo:
作者简介:崔海蓉(1977—),女,博士生;胡小平(联系人),男,博士,副教授,hxpnj@163.com.
基金项目:国家自然科学基金资助项目(70671025).
引文格式: 崔海蓉,胡小平.基于GMD的隐含最小距离风险中性概率测度提取[J].东南大学学报:自然科学版,2011,41(1):210-214.[doi:10.3969/j.issn.1001-0505.2011.01.041]
更新日期/Last Update: 2011-01-20