关于期权定价的几个模型
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摘要
期权是20世纪金融衍生市场创新的成功典范。期权市场已经成为国际金融市场的一个重要部分。本文介绍了期权定价理论的发展历程,并且详细介绍了几种重要的模型,包括Black-Scholes模型,二叉树模型,跳跃扩散模型和随机波动率模型,和Levy过程模型,我们还介绍了倒向随机微分方程在期权定价中的应用。对各种模型做了客观的评价,并展望了未来期权定价理论的发展方向。
Option was the successful innovative example of the financial derivative market in the 20th century. And options market is an important part of the global financial market. In this paper, we introduced the development of options pricing theory, and some main models in detail, including Black-Scholes model, BOPM, jump diffusion model, stochastic volatility model, and Levy process model. We also introduced the application of the backward stochastic differential equations in options pricing. We evaluated the above models objectively, and envisaged the future of options pricing.
Option was the successful innovative example of the financial derivative market in the 20th century. And options market is an important part of the global financial market. In this paper, we introduced the development of options pricing theory, and some main models in detail, including Black-Scholes model, BOPM, jump diffusion model, stochastic volatility model, and Levy process model. We also introduced the application of the backward stochastic differential equations in options pricing. We evaluated the above models objectively, and envisaged the future of options pricing.
引文
[1]Black F. Scholes M. The pricing of options and corporate liabilities [J]. Journal of Political Economy,1973,81(3):637-664.
[2]CoxJC, Ross S A, Rubinstein M. Option pricing:a simplified approach [J]. Journal of Financial Economies,1979,9(7):229-263.
[3]Merton R Theory of rational option pricing [J]. Belt Journal of Economics and Management Science,1973,4(1):141-183.
[4]Cox J, Ross S. The valuation of options for alternation stochastic processes [J]. Journal of Financial Economics,1976,3(3):145-166.
[5]Rubinstein M. The valuation of uncertain income screams and the pricing of options [J]. Bell Journal of Economics and Management Science,1976,7(2):407-425.
[6]CoxJ. Ross S. A survey of some new results in financial option pricing theory[J]. Journal of Financial,1976,31(2):383-402.
[7]Hull J C. Options, futures, and other derivative securities[M] Englewood Cliffs, NJ: Prentice-Hall Inc.,1993.
[8]D. R. Cox, andH. D. Miller. The Theory of Stochastic Processes[M]. London:Cham-pan & Hall,1965.
[9]Merton R C. Option pricing when underlying stock return are discontinuous[J]. Journal of Economics,1976,4(3):125-144.
[10]J. C. Hull. Options, Futures, and Other Derivatives Securities[M]. Prentice Hall, Engle-woodClis, New Jersey,1996.
[11]Musielam, Rutkowsk M. Martingale methods in Financial modeling [M]. Berlin Heidelberg New York:Springer,1997.
[12]C. W. Smith. Option Pricing:AReview[J]. Journal of Financial Economics,1976, 4(26)33-54.
[13]Alan Lewis. Option Valuation under Stochastic Volatility. Finance press,2000.
[14]Peng S. Backward Stochastic Differential Equations and Applications to Optimal Control [J]. Appl. Math. Optim,1993,27; 125-144.
[15]John C. Cox, Jonathan E. Ingersoll, Stephen A. Ross.. An analysis of variable rate loan contracts. The Journal of Finance,35:389-403,1980.
[16]Knut K, AASE. Contingent claims valuation when the security price is combination of an Ito process and a random point process[J]. Stochastic processes and their Applications,1988; 28(2):185-220.
[17]Hull. J. and A. White. The pricing of opions on assets with stochastic volatilities, Journal of Finance.42(1987)
[18]Chan T. Pricing contingent claims on stocks driven by Levy processes[J]. Annals of Appl Prob,1999; 9(2):504-528.
[19]Kallsen Jan. Optimal portfolios for exponential Levy processes[J]. Math Meth Oper Res, 2000; 51(3):357-374.
[20]Bladt M,Rydberg T H. An actuarial approach to option pricing under the physical measure and without market assumptions[J]. Insurance:Mathematics and Economics,1998; 22(1): 65-73.
[21]Martin Schweizer. Option heading for semi. martingales[J]. Stochastic Processes and Their Application,1991; 37(3):339-360.
[22]H. R. Stoll, and R. E. Whaley. New Option Instruments; Arbitrageable Linkages and Valuation [J]. Advances in Futures and Options Research (1986):25-62.
[23]N. Biger, andJ. Hull. The Valuation of Currency Options[J]. Financial Management, 12(1983):24-28.
[24]Maghsoodi. Y. Closed-form solution of the log-normal stochastic volatility option problem I:martingale volatility (1998).
[25]K. Amin, andR. A. Jarrow. Pricing Foreing Currency Options under Stochastic Interest Rates[J]. Journal of International Money and Fomance,10(1991):310-329.
[26]Steven L. Heston. A simple new formula for options with stochastic volatility. Washington University of St. Louis working paper,1999.
[27]FamaE. F. The Behavior of Stock Prices[J]. Journal of Business,38(1965):34-105.
[28]黄志远,随机分析学基础(第二版)[M],科学出版社2001年3月.
[29]钱晓松.跳扩散模型中的测度变换与期权定价.应用概率统计.2004,20(1)：91-99.
[30]林建忠,叶中行.一类跳跃扩散型股价过程组欧式未定权益定价.应用概率统计.2002,18(2)：167-172.
[31]Hull JC.期权、期货和衍生证券[M].张陶伟译.北京：华夏出版社,1997.205-252.
[32]孙健.金融衍生品定价模型.北京：中国经济出版社出版社,2007.
[33]Joseph Stampfli, Victor Goodman.金融数学.蔡明超译.北京：机械工业出版社,2004.
[34]姜礼尚,期权定价的数学模型和方法[M],高等教育出版社,2003,277-290.
[35]陆金甫,关治,偏微分方程数值解法(第2版)[M],2004.
[36]刘金宝.金融工程核心工具-期权[M].上海：文汇出版社,1998.
[37]刘金宝.金融工程技术运用[M].上海：文汇出版社,1998.
[38]宋逢明著.金融工程原理·无套利均衡分析[M].清华大学出版社,1998.
[39]叶中行,林建忠编著.数理金融-资产定价与金融决策理论[M].科学出版社,1998.
[40]张志强著.期权理论与公司理财[M].华夏出版社,2000.
[41]陈松男.金融工程学[M].上海：复旦大学出版社,2002.
[42]陈舜.期权定价理论及其应用[M].北京：中国金融出版社,1998.
[43]胡继之.金融衍生品及其风险管理[J].上海铁道大学学报,1999,20(6)：71-73.
[44]姜伟.金融衍生市场投资理论与实务[M].上海：复旦大学出版社,1996.
[2]CoxJC, Ross S A, Rubinstein M. Option pricing:a simplified approach [J]. Journal of Financial Economies,1979,9(7):229-263.
[3]Merton R Theory of rational option pricing [J]. Belt Journal of Economics and Management Science,1973,4(1):141-183.
[4]Cox J, Ross S. The valuation of options for alternation stochastic processes [J]. Journal of Financial Economics,1976,3(3):145-166.
[5]Rubinstein M. The valuation of uncertain income screams and the pricing of options [J]. Bell Journal of Economics and Management Science,1976,7(2):407-425.
[6]CoxJ. Ross S. A survey of some new results in financial option pricing theory[J]. Journal of Financial,1976,31(2):383-402.
[7]Hull J C. Options, futures, and other derivative securities[M] Englewood Cliffs, NJ: Prentice-Hall Inc.,1993.
[8]D. R. Cox, andH. D. Miller. The Theory of Stochastic Processes[M]. London:Cham-pan & Hall,1965.
[9]Merton R C. Option pricing when underlying stock return are discontinuous[J]. Journal of Economics,1976,4(3):125-144.
[10]J. C. Hull. Options, Futures, and Other Derivatives Securities[M]. Prentice Hall, Engle-woodClis, New Jersey,1996.
[11]Musielam, Rutkowsk M. Martingale methods in Financial modeling [M]. Berlin Heidelberg New York:Springer,1997.
[12]C. W. Smith. Option Pricing:AReview[J]. Journal of Financial Economics,1976, 4(26)33-54.
[13]Alan Lewis. Option Valuation under Stochastic Volatility. Finance press,2000.
[14]Peng S. Backward Stochastic Differential Equations and Applications to Optimal Control [J]. Appl. Math. Optim,1993,27; 125-144.
[15]John C. Cox, Jonathan E. Ingersoll, Stephen A. Ross.. An analysis of variable rate loan contracts. The Journal of Finance,35:389-403,1980.
[16]Knut K, AASE. Contingent claims valuation when the security price is combination of an Ito process and a random point process[J]. Stochastic processes and their Applications,1988; 28(2):185-220.
[17]Hull. J. and A. White. The pricing of opions on assets with stochastic volatilities, Journal of Finance.42(1987)
[18]Chan T. Pricing contingent claims on stocks driven by Levy processes[J]. Annals of Appl Prob,1999; 9(2):504-528.
[19]Kallsen Jan. Optimal portfolios for exponential Levy processes[J]. Math Meth Oper Res, 2000; 51(3):357-374.
[20]Bladt M,Rydberg T H. An actuarial approach to option pricing under the physical measure and without market assumptions[J]. Insurance:Mathematics and Economics,1998; 22(1): 65-73.
[21]Martin Schweizer. Option heading for semi. martingales[J]. Stochastic Processes and Their Application,1991; 37(3):339-360.
[22]H. R. Stoll, and R. E. Whaley. New Option Instruments; Arbitrageable Linkages and Valuation [J]. Advances in Futures and Options Research (1986):25-62.
[23]N. Biger, andJ. Hull. The Valuation of Currency Options[J]. Financial Management, 12(1983):24-28.
[24]Maghsoodi. Y. Closed-form solution of the log-normal stochastic volatility option problem I:martingale volatility (1998).
[25]K. Amin, andR. A. Jarrow. Pricing Foreing Currency Options under Stochastic Interest Rates[J]. Journal of International Money and Fomance,10(1991):310-329.
[26]Steven L. Heston. A simple new formula for options with stochastic volatility. Washington University of St. Louis working paper,1999.
[27]FamaE. F. The Behavior of Stock Prices[J]. Journal of Business,38(1965):34-105.
[28]黄志远,随机分析学基础(第二版)[M],科学出版社2001年3月.
[29]钱晓松.跳扩散模型中的测度变换与期权定价.应用概率统计.2004,20(1)：91-99.
[30]林建忠,叶中行.一类跳跃扩散型股价过程组欧式未定权益定价.应用概率统计.2002,18(2)：167-172.
[31]Hull JC.期权、期货和衍生证券[M].张陶伟译.北京：华夏出版社,1997.205-252.
[32]孙健.金融衍生品定价模型.北京：中国经济出版社出版社,2007.
[33]Joseph Stampfli, Victor Goodman.金融数学.蔡明超译.北京：机械工业出版社,2004.
[34]姜礼尚,期权定价的数学模型和方法[M],高等教育出版社,2003,277-290.
[35]陆金甫,关治,偏微分方程数值解法(第2版)[M],2004.
[36]刘金宝.金融工程核心工具-期权[M].上海：文汇出版社,1998.
[37]刘金宝.金融工程技术运用[M].上海：文汇出版社,1998.
[38]宋逢明著.金融工程原理·无套利均衡分析[M].清华大学出版社,1998.
[39]叶中行,林建忠编著.数理金融-资产定价与金融决策理论[M].科学出版社,1998.
[40]张志强著.期权理论与公司理财[M].华夏出版社,2000.
[41]陈松男.金融工程学[M].上海：复旦大学出版社,2002.
[42]陈舜.期权定价理论及其应用[M].北京：中国金融出版社,1998.
[43]胡继之.金融衍生品及其风险管理[J].上海铁道大学学报,1999,20(6)：71-73.
[44]姜伟.金融衍生市场投资理论与实务[M].上海：复旦大学出版社,1996.