期权理论在处置我国不良资产问题中的应用与研究
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摘要
本文运用期权分析的方法，结合Black-Scholes模型和二叉树模型对不良资产的处置问题进行了研究。主要工作包括：
(1)期权定价理论和不良资产处置理论的研究分析；
(2)不良资产股权化问题的研究分析；
(3)不良资产债券化问题的研究分析。
对于期权定价理论和不良资产处置理论，我们研究了Black-Scholes模型及其推广、二叉树模型以及二者的比较，得出两者实质是一致的；我们研究了不良资产的成因、现状和当前的处置方法，发现股权化和债券化是一种趋势。
对于不良资产股权化，分别用Black-Scholes模型和二叉树模型研究了债权转换股权的比例测算，得出转换比例公式，并通过修正，得出非上市公司和含股权回购合约的理性定价比例；研究了债权转换股权企业的风险度量，给出了单一公司和多个公司的风险度量公式；研究了债权转换股权企业的风险控制，给出了亏损概率公式；研究了债权转换股权企业的效果分析，给出了一个评估效果分析标准。
对于不良资产债券化，我们研究了公司股票的估价和公司债券的估价，并对可转换债券进行期权分析，得出了可转换债券的定价公式。
In this thesis, the method of the option analyse was adopted to studythe problem of bad assets by Black-Scholes model and Binomial model.The main work including:
(a) the study and analyse of the option pricing theory and thedisposition theory of bad assets;
(b) the study and analyse of stocklization;
(c) the study and analyse of bondlization.
For the option pricing theory and the disposition theory of bad assets,Black-Scholes model and its extend, Binomial model and thecomparation of them were studied, and the conclusion that they werevirtually consistent was got; We studied the cause of formation, theactuality and current disposition method of bad assets, and find it was atrend to deal with bad assets by stocklization and bondlization.
For stocklization, we studied the proportion calculating of changingcreditor's rights into stock right separately using Black-Scholes modeland Binomial model, and the conversion proportion formula was set up.Via revises, we gained the rational pricing proportion of corporation ofnon-coming into the market and containing stock right back purchaseagreement; We analysed the risk measure of changing creditor's rightsinto stock right, and the risk measure formula of single company andmulti-company was founded; The risk controlling method for changing creditor's rights into stock right and the bankrupt probability formulawere got; The result analysis for changing creditor's rights into stockright and a standard of evaluating the result analysis were shown.
For the bond, the appraisal of company's stock, the appraisal ofcompany's bond and the option analysis of the convertible bond wereinvestigated, and the pricing formula of the convertible bond was gained.
(1)期权定价理论和不良资产处置理论的研究分析；
(2)不良资产股权化问题的研究分析；
(3)不良资产债券化问题的研究分析。
对于期权定价理论和不良资产处置理论，我们研究了Black-Scholes模型及其推广、二叉树模型以及二者的比较，得出两者实质是一致的；我们研究了不良资产的成因、现状和当前的处置方法，发现股权化和债券化是一种趋势。
对于不良资产股权化，分别用Black-Scholes模型和二叉树模型研究了债权转换股权的比例测算，得出转换比例公式，并通过修正，得出非上市公司和含股权回购合约的理性定价比例；研究了债权转换股权企业的风险度量，给出了单一公司和多个公司的风险度量公式；研究了债权转换股权企业的风险控制，给出了亏损概率公式；研究了债权转换股权企业的效果分析，给出了一个评估效果分析标准。
对于不良资产债券化，我们研究了公司股票的估价和公司债券的估价，并对可转换债券进行期权分析，得出了可转换债券的定价公式。
In this thesis, the method of the option analyse was adopted to studythe problem of bad assets by Black-Scholes model and Binomial model.The main work including:
(a) the study and analyse of the option pricing theory and thedisposition theory of bad assets;
(b) the study and analyse of stocklization;
(c) the study and analyse of bondlization.
For the option pricing theory and the disposition theory of bad assets,Black-Scholes model and its extend, Binomial model and thecomparation of them were studied, and the conclusion that they werevirtually consistent was got; We studied the cause of formation, theactuality and current disposition method of bad assets, and find it was atrend to deal with bad assets by stocklization and bondlization.
For stocklization, we studied the proportion calculating of changingcreditor's rights into stock right separately using Black-Scholes modeland Binomial model, and the conversion proportion formula was set up.Via revises, we gained the rational pricing proportion of corporation ofnon-coming into the market and containing stock right back purchaseagreement; We analysed the risk measure of changing creditor's rightsinto stock right, and the risk measure formula of single company andmulti-company was founded; The risk controlling method for changing creditor's rights into stock right and the bankrupt probability formulawere got; The result analysis for changing creditor's rights into stockright and a standard of evaluating the result analysis were shown.
For the bond, the appraisal of company's stock, the appraisal ofcompany's bond and the option analysis of the convertible bond wereinvestigated, and the pricing formula of the convertible bond was gained.
引文
[1] EBlack and M.Scholes. The Pricing of Options and Corporate Liabilities[J]. Journal of Political Economy, May-June 1973,81:63-87
[2] Cox, J.,S.Ross, M.Rubinstein. Option Pricing:A Simplified Approach[J]. Journal of Financial Economics, October 1979,7:229-264
[3] Scholes,M.S. Taxes and Pricing of Options [J]. Journal of Finance;1976, 31(2):319-332
[4] Merton,R.C. Continuous-time Finance[M]. Oxford:Basil Blackwell. 1990
[5] Merton, R.C. Theory of Rational Option Pricing[J]. Bell Journal of Economics and Manage ment Science,Spring 1973,4:141-183
[6] Hull,J.C.,and A.White. The Pricing of Options on assets with Stochastic Volatilities [J]. Journal of Finance,June 1987,42:281-300
[7] 陈守红．可转换债券投融资理论与实务[M]．上海：上海财经大学出版社，2005．10
[8] Karatzas, Shreve, S.E. Brownian Motion and Stochastic Calculus[M]. Springer Verlag, New York, 1992
[9] Karatzas. Optimization Problems in the Theory of Continuous Trading[J]. SIAM J.Control Optim, 1989,27:1221-1259
[10] 马忠智，吕益民．可转换公司债券发行与交易实务[M]．北京：人民出版社，1996．10
[11] John C．Hull(美)，张陶伟译．期权，期货和其它衍生产品[M]．北京：华夏出版社，2000．1
[12] 杨云红．高级金融理论[M]．武汉：武汉大学出版社，2001．3
[13] 叶中行，林建忠．数理金融——资产定价与金融决策理论[M]．北京：科学出版社，1998．12
[14] 刘嘉焜．应用随机过程[M]．北京：科学出版社，2002
[15] A.V.Mei'nikov. Financial Markets[M]. American Mathematical Society, 1999.
[16] Park, H.Y. and A.H.Chen. Differences between Futures and Forward Prices: A Further Investigation of Marking to Market Effects [J]. Journal of Futures Markets, February 1985, 5:77-88
[17] French. A Comparison of Futures and Forward Prices [J]. Journal of Finance Economics, November 1983,12:311-342
[18] Cornell,B. and M.Reinganum. Forward and Futures Prices: Evidence form Foreign change Market s [J]. Journal of Finance,December 1981,36:35-45
[19] 雍炯敏，刘百道．数学金融学．上海：上海人民出版社．2003
[20] R.Geske. The Valuation of Compound Options [J]. Journal of Finance Economics, 1979,7:63-81
[21] R.A.Carmona, E.Cinlar, I.Ekeland. Paris-Princeton Lectures on Mathematical Finance 2002[C]
[22] Amendinger, J., Becherer,D. A monetary value for initial information in portfolio optimization. Finance and Stochastics, 2003, 7,29-46
[23] Amendinger, J. Martingale representation theorems for initially enlarged filtrations. Stoch. Proc. Appl,2000, 89:101-116
[24] 刘海龙，吴冲锋．期权定价方法综述[J]．管理科学学报，2002，5(2)：67-73
[25] 于春海．发展中金融市场上的资产定价问题研究[M]．北京：中国经济出版社，2006．3
[26] Zhang, X. L. Numerical analysis of American option pricing in a jumpdiffusion model. Mathematics of Operations Research, 1997,22:668-690
[27] Beltamy, N., Jeanblanc, M. Incompleteness of markets driven by a mixed diffusion. Finance Stochast,2000,4:209-222
[28] Fabrice Baudoin, Laurent Nguyen-Ngoc. The financial value of a weak information on a financial market. Finance Stochast,2004,8:415-435
[29] Schachermayer, W. Martingale measures for discrete-time processes with infinite horizon. Math. Finance, 1994,4:25-55
[30] Jouini, E., Kallal, H. Martingales and arbitrage in securities markets with transaction costs. J. Econ. Theo, 1995,66:178-197
[31] Lisa A. Korf. Stochastic programming duality: L∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Program., Ser. A,2004,99:241-259
[32] Pikovsky, I.. Market equilibrium with di_erential information. Finance Stochastics, to appear, 1997
[33] Korn, R.. Optimal Portfolios. World Scienti_c, Singapore,1998
[34] 俞迎达，俞苗．Black-Scholes期权定价模型的简化推导[J]．数学的实践与认识，2001，31(6)：756—758
[35] 陈万义．非风险中性定价意义下的欧式期权定价公式[J]．数学的实践与认识，2004．34(1)：176-179
[36] Zitkovic, G. A ltered version of the bipolar theorem of Brannath and chachermayer. J. Theoret. Probab. 15(1), 41-61 (2002)
[37] Brennan, M. J., and Schwartz, E. S., A Continuous Time Approach to the Pricing of Bonds [J]. Journal of Banking and Finance, July 1979, 2:133-155
[38] Brennan, M.J. and Schwartz, E.S., Analyzing Convertible Securities[J]. Journal of Financial and Quantitative Analysis, XV, November 1980, 4:907-929
[39] Merton R. C, On the pricing of corporate debt: the risk structure of interest rates[J]. Journal of Finance29, 1974
[40] Hull J. C., Options, futures, and other deritives (4thed.) [M] Pretice Hall, 2000.3
[41] Saunders A., Financial institutions management (3thed.) [M]. McGraw-Hill Companies, 2000
[42] Davis M. Lischa F., Convertible bonds with market risk and credit risk[R]. Tokyo-Mitsubishi international, 1999
[43] Duffle D. and Singletton K. J., Modeling termstructures of dufaultable bonds[J]. Review of Finacial Studies, 1999, 2
[44] Tsiveriotis K, Fernandes C. Valuing convertible bonds with credit risk. Journal of Fixed Income, 1998, 8(3):95-102
[45] Mayers, D. Why firms issue convertible bonds:the matching of financial and real investment options. Journal of Financial Economics 47, 1998
[46] Ammann M, Horst J, Veld C. An empirical analysis of pricing Dutch reverse convertible bonds[D]. Tilburg University, Working paper, 2003
[47] Takahashi A, Kobayashi T, Nakagawa N. Pricing Convertible Bonds with Default Risk[J]. Journal of Fixed Income, 2001, 11:20-29
[48] Bloch D, Miralles P. Credit Treatment in Convertible Bond Model[D]. Dresdner Kleinwort Wasserstein, Working Paper, 2002
[49] Ayache E, Forsyth P, Vetzal K. The Valuation of Convertible Bonds with Credit Risk[D], Uiniversity of Waterloo, Working Paper, 2002
[50] Tsveriotis K and Fernandes C., Valuing convertible bonds with credit risk[J]. Juornal of Fixedlncome, 1998, 9(8)
[51] Ayache E., Forsyth P. A. and Vetzal K. R., The valuation of convertible bonds with credit risk[J]. Juornalof Fixedlncome, 2002, 5
[52] TakaHashi, KobayashiAT, NakagawaN. Pricing convertible bonds with default risk[J]. JuornalofFixedlncome, 2001, 11 (11)
[53] YigitbasiogluAB., Pricing convertible bonds with interest rate, equity, credit and Fxrisk[R].ISMACenter, UniversityofReading,2001,14
[54] 刘海龙，吴冲锋。期权定价方法综述[J]．管理科学学报，2002，5(2)：67-73
[55] 达雷尔·达菲．动态资产定价理论[M]．上海：上海财经大学出版社，2004．5
[56] 秦学志．金融工程原理与应用研究[M]．大连：大连理工大学出版社，2005．11
[57] 张彩玉．期权定价的博弈论分析[J]．西南交通大学学报．2003，6：367-370
[58] Joseph Stampfli(美)，Victor Goodman(美)，蔡明超译．金融数学．北京：机械工业出版社，2004．9
[59] 李勇．关于我国不良资产证券化的初步探讨[M]．北京：中国财政经济出版社，2005．1
[60] 于凤坤．资产证券化：理论与实务[M]．北京：北京大学出版社，2002．5
[61] 马忠智，吕益民．可转换公司债券发行与交易实务[M]．北京：人民出版社．1996．10
[62] 张士明．多赢：批量处置不良贷款的成功实践与理论思考[M]．北京：中国金融出版社，2005．2
[2] Cox, J.,S.Ross, M.Rubinstein. Option Pricing:A Simplified Approach[J]. Journal of Financial Economics, October 1979,7:229-264
[3] Scholes,M.S. Taxes and Pricing of Options [J]. Journal of Finance;1976, 31(2):319-332
[4] Merton,R.C. Continuous-time Finance[M]. Oxford:Basil Blackwell. 1990
[5] Merton, R.C. Theory of Rational Option Pricing[J]. Bell Journal of Economics and Manage ment Science,Spring 1973,4:141-183
[6] Hull,J.C.,and A.White. The Pricing of Options on assets with Stochastic Volatilities [J]. Journal of Finance,June 1987,42:281-300
[7] 陈守红．可转换债券投融资理论与实务[M]．上海：上海财经大学出版社，2005．10
[8] Karatzas, Shreve, S.E. Brownian Motion and Stochastic Calculus[M]. Springer Verlag, New York, 1992
[9] Karatzas. Optimization Problems in the Theory of Continuous Trading[J]. SIAM J.Control Optim, 1989,27:1221-1259
[10] 马忠智，吕益民．可转换公司债券发行与交易实务[M]．北京：人民出版社，1996．10
[11] John C．Hull(美)，张陶伟译．期权，期货和其它衍生产品[M]．北京：华夏出版社，2000．1
[12] 杨云红．高级金融理论[M]．武汉：武汉大学出版社，2001．3
[13] 叶中行，林建忠．数理金融——资产定价与金融决策理论[M]．北京：科学出版社，1998．12
[14] 刘嘉焜．应用随机过程[M]．北京：科学出版社，2002
[15] A.V.Mei'nikov. Financial Markets[M]. American Mathematical Society, 1999.
[16] Park, H.Y. and A.H.Chen. Differences between Futures and Forward Prices: A Further Investigation of Marking to Market Effects [J]. Journal of Futures Markets, February 1985, 5:77-88
[17] French. A Comparison of Futures and Forward Prices [J]. Journal of Finance Economics, November 1983,12:311-342
[18] Cornell,B. and M.Reinganum. Forward and Futures Prices: Evidence form Foreign change Market s [J]. Journal of Finance,December 1981,36:35-45
[19] 雍炯敏，刘百道．数学金融学．上海：上海人民出版社．2003
[20] R.Geske. The Valuation of Compound Options [J]. Journal of Finance Economics, 1979,7:63-81
[21] R.A.Carmona, E.Cinlar, I.Ekeland. Paris-Princeton Lectures on Mathematical Finance 2002[C]
[22] Amendinger, J., Becherer,D. A monetary value for initial information in portfolio optimization. Finance and Stochastics, 2003, 7,29-46
[23] Amendinger, J. Martingale representation theorems for initially enlarged filtrations. Stoch. Proc. Appl,2000, 89:101-116
[24] 刘海龙，吴冲锋．期权定价方法综述[J]．管理科学学报，2002，5(2)：67-73
[25] 于春海．发展中金融市场上的资产定价问题研究[M]．北京：中国经济出版社，2006．3
[26] Zhang, X. L. Numerical analysis of American option pricing in a jumpdiffusion model. Mathematics of Operations Research, 1997,22:668-690
[27] Beltamy, N., Jeanblanc, M. Incompleteness of markets driven by a mixed diffusion. Finance Stochast,2000,4:209-222
[28] Fabrice Baudoin, Laurent Nguyen-Ngoc. The financial value of a weak information on a financial market. Finance Stochast,2004,8:415-435
[29] Schachermayer, W. Martingale measures for discrete-time processes with infinite horizon. Math. Finance, 1994,4:25-55
[30] Jouini, E., Kallal, H. Martingales and arbitrage in securities markets with transaction costs. J. Econ. Theo, 1995,66:178-197
[31] Lisa A. Korf. Stochastic programming duality: L∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Program., Ser. A,2004,99:241-259
[32] Pikovsky, I.. Market equilibrium with di_erential information. Finance Stochastics, to appear, 1997
[33] Korn, R.. Optimal Portfolios. World Scienti_c, Singapore,1998
[34] 俞迎达，俞苗．Black-Scholes期权定价模型的简化推导[J]．数学的实践与认识，2001，31(6)：756—758
[35] 陈万义．非风险中性定价意义下的欧式期权定价公式[J]．数学的实践与认识，2004．34(1)：176-179
[36] Zitkovic, G. A ltered version of the bipolar theorem of Brannath and chachermayer. J. Theoret. Probab. 15(1), 41-61 (2002)
[37] Brennan, M. J., and Schwartz, E. S., A Continuous Time Approach to the Pricing of Bonds [J]. Journal of Banking and Finance, July 1979, 2:133-155
[38] Brennan, M.J. and Schwartz, E.S., Analyzing Convertible Securities[J]. Journal of Financial and Quantitative Analysis, XV, November 1980, 4:907-929
[39] Merton R. C, On the pricing of corporate debt: the risk structure of interest rates[J]. Journal of Finance29, 1974
[40] Hull J. C., Options, futures, and other deritives (4thed.) [M] Pretice Hall, 2000.3
[41] Saunders A., Financial institutions management (3thed.) [M]. McGraw-Hill Companies, 2000
[42] Davis M. Lischa F., Convertible bonds with market risk and credit risk[R]. Tokyo-Mitsubishi international, 1999
[43] Duffle D. and Singletton K. J., Modeling termstructures of dufaultable bonds[J]. Review of Finacial Studies, 1999, 2
[44] Tsiveriotis K, Fernandes C. Valuing convertible bonds with credit risk. Journal of Fixed Income, 1998, 8(3):95-102
[45] Mayers, D. Why firms issue convertible bonds:the matching of financial and real investment options. Journal of Financial Economics 47, 1998
[46] Ammann M, Horst J, Veld C. An empirical analysis of pricing Dutch reverse convertible bonds[D]. Tilburg University, Working paper, 2003
[47] Takahashi A, Kobayashi T, Nakagawa N. Pricing Convertible Bonds with Default Risk[J]. Journal of Fixed Income, 2001, 11:20-29
[48] Bloch D, Miralles P. Credit Treatment in Convertible Bond Model[D]. Dresdner Kleinwort Wasserstein, Working Paper, 2002
[49] Ayache E, Forsyth P, Vetzal K. The Valuation of Convertible Bonds with Credit Risk[D], Uiniversity of Waterloo, Working Paper, 2002
[50] Tsveriotis K and Fernandes C., Valuing convertible bonds with credit risk[J]. Juornal of Fixedlncome, 1998, 9(8)
[51] Ayache E., Forsyth P. A. and Vetzal K. R., The valuation of convertible bonds with credit risk[J]. Juornalof Fixedlncome, 2002, 5
[52] TakaHashi, KobayashiAT, NakagawaN. Pricing convertible bonds with default risk[J]. JuornalofFixedlncome, 2001, 11 (11)
[53] YigitbasiogluAB., Pricing convertible bonds with interest rate, equity, credit and Fxrisk[R].ISMACenter, UniversityofReading,2001,14
[54] 刘海龙，吴冲锋。期权定价方法综述[J]．管理科学学报，2002，5(2)：67-73
[55] 达雷尔·达菲．动态资产定价理论[M]．上海：上海财经大学出版社，2004．5
[56] 秦学志．金融工程原理与应用研究[M]．大连：大连理工大学出版社，2005．11
[57] 张彩玉．期权定价的博弈论分析[J]．西南交通大学学报．2003，6：367-370
[58] Joseph Stampfli(美)，Victor Goodman(美)，蔡明超译．金融数学．北京：机械工业出版社，2004．9
[59] 李勇．关于我国不良资产证券化的初步探讨[M]．北京：中国财政经济出版社，2005．1
[60] 于凤坤．资产证券化：理论与实务[M]．北京：北京大学出版社，2002．5
[61] 马忠智，吕益民．可转换公司债券发行与交易实务[M]．北京：人民出版社．1996．10
[62] 张士明．多赢：批量处置不良贷款的成功实践与理论思考[M]．北京：中国金融出版社，2005．2