|Table of Contents|

[1] Hu Xiaoping, Cui Hairong, Zhu Lihua, et al. Recovering implied risk-neutral probability density functionusing SVR [J]. Journal of Southeast University (English Edition), 2010, 26 (3): 489-493. [doi:10.3969/j.issn.1003-7985.2010.03.024]
Copy

Recovering implied risk-neutral probability density functionusing SVR()
基于SVR的隐含风险中性概率密度函数提取
Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
26
Issue:
2010 3
Page:
489-493
Research Field:
Economy and Management
Publishing date:
2010-09-30

Info

Title:
Recovering implied risk-neutral probability density functionusing SVR
基于SVR的隐含风险中性概率密度函数提取
Author(s):
Hu Xiaoping1;  Cui Hairong1;  2;  Zhu Lihua1;  Wang Xinyan1
1 School of Economics and Management, Southeast University, Nanjing 211189, China
2 College of Engineering, Nanjing Agricultural University, Nanjing 210032, China
胡小平1;  崔海蓉1;  2;  朱丽华1;  王新燕1
1东南大学经济管理学院, 南京 211189; 2南京农业大学工学院, 南京 210032
Keywords:
support vector regression;  option prices;  implied risk-neutral probability;  linear operator equation;  non-parametric method
支持向量回归机;  期权价格;  隐含风险中性概率;  线性算子方程;  非参数方法
PACS:
F830.9
DOI:
10.3969/j.issn.1003-7985.2010.03.024
Abstract:
Using support vector regression(SVR), a novel non-parametric method for recovering implied risk-neutral probability density function(IRNPDF)is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.
利用支持向量回归机(SVR), 通过求解线性算子方程, 提出了一种全新的非参数类恢复隐含风险中性概率密度函数的方法.首先, 介绍了支持向量回归机应用于函数逼近的基本原理, 当仅知算子方程右边函数的一些函数值而不知其函数形式时, 描述了基于支持向量回归机的线性算子方程求解方法.然后, 给出了基于支持向量回归机的隐含风险中性概率密度函数求解原理及交叉核函数的构建方法.最后, 通过实证研究, 验证了该方法的有效性.研究结果表明, 所提方法克服了传统参数类方法对期权执行价格有严格限制的缺陷, 同时对数据量的要求也比其他非参数类方法少, 是一种很有前景的还原隐含风险中性概率方法与手段.

References:

[1] Jackwerth J C. Option implied risk-neutral distributions and implied binomial trees: a literature review [J]. Journal of Derivatives, 1999, 7(2): 66-82.
[2] Shimko D. Bounds of probability [J]. Risk, 1993, 6(4): 33-37.
[3] Bates D S. The crash of ’87: Was it expected? The evidence from options markets[J]. Journal of Finance, 1991, 46(1): 1009-1044.
[4] Bliss R, Panigirtzoglou N. Testing the stability of implied probability density functions [J]. Journal of Banking and Finance, 2002, 26(1): 381-422.
[5] Duffie D, Pan J, Singleton K. Transform analysis and asset pricing for affine jump-diffusions[J]. Econometrica, 2000, 68(1): 1343-1376.
[6] 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, 1997, 32(1): 91-115.
[7] Aït-Sahalia Y, Lo A W. Nonparametric estimation of state-price densities implicit in financial asset prices[J]. Journal of Finance, 1998, 53(1): 499-547.
[8] 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(1): 851-889.
[9] Garcia R, Gencay R. Pricing and hedging derivative securities with neural networks and a homogeneity hint [J]. Journal of Econometrics, 2000, 94(1/2): 93-115.
[10] Gibson R, Gencay R. Model risk for European-style stock index options[J]. IEEE Transactions on Neural Networks, 2007, 22(18): 193-202.
[11] 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.
[12] Galati G, Melick W, Micu M. Foreign exchange market intervention and expectations: the yen/dollar exchange rate[J]. Journal of International Money and Finance, 2005, 24(6): 982-1011.
[13] Milne F, Madan D. Contingent claims valued and hedged by pricing and investing in a basis[J]. Mathematical Finance, 1994, 4(3): 223-245.
[14] Corrado C J, Su T. Implied volatility skews and stock index skewness and kurtosis implied by S& P 500 index option prices[J]. The Journal of Derivatives, 1997, 4(4): 8-19.
[15] 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.
[16] Bahra B. Implied risk-neutral probability density functions from option prices: theory and application[EB/OL].(1997-07)[2010-02-26]. http://ssrn.com/abstract=77429.
[17] Vapnik V N. Statistical learning theory[M]. New York: Wiley, 1998.
[18] Mikhlin S G. Mathematical physics and technology[M]. London: Pergamon Press, 1964.

Memo

Memo:
Biography: Hu Xiaoping(1971—), male, doctor, associate professor, hxpnj@163.com.
Foundation item: The National Natural Science Foundation of China(No.70671025).
Citation: Hu Xiaoping, Cui Hairong, Zhu Lihua, et al.Recovering implied risk-neutral probability density function using SVR[J].Journal of Southeast University(English Edition), 2010, 26(3):489-493.
Last Update: 2010-09-20