欧式及美式“巴黎期权”定价模型仿真与优化
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摘要
衍生品是一种金融工具,它们的到期日的损益依赖于基础资产,其基础资产可以是股票,股票指数,期货,利率等。在金融市场的不断发展过程中,出现了大量满足投资者需要的全新衍生证券。而一些衍生证券复杂的特性,决定了其定价的难度。
路径相关的期权合同是其中最难定价的。它们到期日的损益极大程度地依赖于基础资产的价格路径。本论文主要是建立了一种美式及欧式巴黎期权的定价模型及相关定价技术。这种期权合同有处理路径相关的特性,此外它的到期期限是不断变化的。文章针对累积式与连续式巴黎期权作出定价,应用随机过程理论,三叉树模型,并通过C++编程实现期权价格的计算,最后对计算结果以及仿真效果作出了分析。
A derivative is a financial instrument whose payoff depends on an underlying asset, such as a stock or a future contract. As the financial market becomes more prosperous, various new derivatives are designed to fulfill the needs of investors. Some derivatives are complicated in their terms, and give rise to problems in valuation.
A path-dependent option is among all, the most complicated derivative in its valuation. The terminal payoff for an option of such type depends critically on the price path of its underlying financial instrument. In this thesis we develop pricing techniques for American and European Parisian type options. These options have path-dependent feature and their terms vary. We focus on the pricing of consecutive and cumulative Parisian-type options using an adapted trinomial tree model implemented in a C++ program and we present the numerical results obtained with this technique.
路径相关的期权合同是其中最难定价的。它们到期日的损益极大程度地依赖于基础资产的价格路径。本论文主要是建立了一种美式及欧式巴黎期权的定价模型及相关定价技术。这种期权合同有处理路径相关的特性,此外它的到期期限是不断变化的。文章针对累积式与连续式巴黎期权作出定价,应用随机过程理论,三叉树模型,并通过C++编程实现期权价格的计算,最后对计算结果以及仿真效果作出了分析。
A derivative is a financial instrument whose payoff depends on an underlying asset, such as a stock or a future contract. As the financial market becomes more prosperous, various new derivatives are designed to fulfill the needs of investors. Some derivatives are complicated in their terms, and give rise to problems in valuation.
A path-dependent option is among all, the most complicated derivative in its valuation. The terminal payoff for an option of such type depends critically on the price path of its underlying financial instrument. In this thesis we develop pricing techniques for American and European Parisian type options. These options have path-dependent feature and their terms vary. We focus on the pricing of consecutive and cumulative Parisian-type options using an adapted trinomial tree model implemented in a C++ program and we present the numerical results obtained with this technique.
引文
[1]CHESNEY M.,JEANBLANC-PICQUE M.AND YOR M.,Parisian Options and Excursion Theory,Advances in Applied Probabilities,March 1997.
[2]FUSAI G.AND TAGLIANI A.,Pricing of Occupation Time Derivatives:Continuous and Discrete Monitoring,Journal of Computational Finance,5(1),Fall 2001,pp.1-37.
[3]HUGONNIER J.,The Feynman-Kac Formula and Pricing Occupation Times Derivatives,International Journal of Theoretical and Applied Finance,2(2),1999,pp.153-178.
[4]HABER R.J.,SCHONBUCHER P.J.AND WILMOTT P.,Pricing Parisian Options,The Journal of Derivatives,Spring 1998,pp.71-79.
[5]LABART C.AND LELONG J..Pricing double barrier Parisian Options using Laplace transforms.Ecole Polytechnique,November 2006
[6]TIAN Y.S.,A Flexible Binomial Option Pricing Model,The Journal of Futures Markets,19(7),1999,pp.817-843.
[7]BABBS S.,Binomial Valuation of Lookback Options,Journal of Economic Dynamics & Control 24,pp.1499-1525.
[8]HSUEH L.P.AND LIU Y.A.,Step-Reset Options:Design and Valuation,The Journal of Futures Markets 22(2),2002,pp.155-171.
[9]COSTABILE M.,Extending the Cox-Ross-Rubinstein algorithm for pricing options with exponential boundaries.University of Calabria,2002.
[10]GUSTAFSON M..AND JETLEY G,A Hybrid Approach to Valuing American Parisian Options,http://ssrn.com/abstract=998599,2003.
[11]CHESNEY M.AND GAUTHIER L.,American Parisian Options,Finance and Stochastics,Vol.10,2006,pp.475-506.
[12]LABART C.AND LELONG J.,Pricing Parisian Options,Ecole Polytechnique,December 2005
[13]FORSYTH P.,An Introduction to Computational Finance Without Agonizing Pain,University of Waterloo,February 2007.
[14]Y.LAI AND J.SPANIER,Applications of Monte Carlo/Quasi-Monte Carlo Methods in Finance:Option Pricing,Claremont Graduate University,2000.
[15]HULL J.,Options,futures and other derivatives,Prentice-Hall,1997,ISBN 0-13-186479-3.
[16]DUFFY D.,Financial Instrument Pricing using C++,John Wiley &Sons,2004,ISBN 0-47-085509-6.
[17]MORAUX F.,On cumulative Parisian Options,Finance,vol.23,2002,pp.127-132.
[18]RUBINSTEIN M.,On the Relation Between Binomial and Trinomial Option Pricing Models,Journal of Derivatives,Winter 2000.
[19]VAN DER MEU M.,SCHOUTEN D.AND ELIENS A.,Design Patterns for Derivatives Software.Vrije University - Amsterdam,2000.
[20]BARONE-ADESI G.,FUSARI N.AND THEAL J.,Barrier Option Pricing Using Adjusted Transition Probabilities,University of Lugano,May 2007.
[21]VETZAL K.R.AND FORSYTH P.A.,Discrete Parisian and delayed barrier options:a general numerical approach,Advances in Futures and Options Research 10,pp.1-15.
[22]DAVIS M.,Mathematics of Financial Markets,Mathematics Unlimited -2001& Beyond.Springer,Berlin,Austrian Science Foundation,2000.
[23]RITCHKEN P.,On Pricing Barrier Options,The Journal of Derivatives,Winter 1995,pp.19-28.
[24]DERMAN E.,KANI I.AND CHRISS N.,Implied Trinomial Trees of the Volatility Smile,Goldman Sachs - Quantitative Strategies Research Notes,February 2006.
[2]FUSAI G.AND TAGLIANI A.,Pricing of Occupation Time Derivatives:Continuous and Discrete Monitoring,Journal of Computational Finance,5(1),Fall 2001,pp.1-37.
[3]HUGONNIER J.,The Feynman-Kac Formula and Pricing Occupation Times Derivatives,International Journal of Theoretical and Applied Finance,2(2),1999,pp.153-178.
[4]HABER R.J.,SCHONBUCHER P.J.AND WILMOTT P.,Pricing Parisian Options,The Journal of Derivatives,Spring 1998,pp.71-79.
[5]LABART C.AND LELONG J..Pricing double barrier Parisian Options using Laplace transforms.Ecole Polytechnique,November 2006
[6]TIAN Y.S.,A Flexible Binomial Option Pricing Model,The Journal of Futures Markets,19(7),1999,pp.817-843.
[7]BABBS S.,Binomial Valuation of Lookback Options,Journal of Economic Dynamics & Control 24,pp.1499-1525.
[8]HSUEH L.P.AND LIU Y.A.,Step-Reset Options:Design and Valuation,The Journal of Futures Markets 22(2),2002,pp.155-171.
[9]COSTABILE M.,Extending the Cox-Ross-Rubinstein algorithm for pricing options with exponential boundaries.University of Calabria,2002.
[10]GUSTAFSON M..AND JETLEY G,A Hybrid Approach to Valuing American Parisian Options,http://ssrn.com/abstract=998599,2003.
[11]CHESNEY M.AND GAUTHIER L.,American Parisian Options,Finance and Stochastics,Vol.10,2006,pp.475-506.
[12]LABART C.AND LELONG J.,Pricing Parisian Options,Ecole Polytechnique,December 2005
[13]FORSYTH P.,An Introduction to Computational Finance Without Agonizing Pain,University of Waterloo,February 2007.
[14]Y.LAI AND J.SPANIER,Applications of Monte Carlo/Quasi-Monte Carlo Methods in Finance:Option Pricing,Claremont Graduate University,2000.
[15]HULL J.,Options,futures and other derivatives,Prentice-Hall,1997,ISBN 0-13-186479-3.
[16]DUFFY D.,Financial Instrument Pricing using C++,John Wiley &Sons,2004,ISBN 0-47-085509-6.
[17]MORAUX F.,On cumulative Parisian Options,Finance,vol.23,2002,pp.127-132.
[18]RUBINSTEIN M.,On the Relation Between Binomial and Trinomial Option Pricing Models,Journal of Derivatives,Winter 2000.
[19]VAN DER MEU M.,SCHOUTEN D.AND ELIENS A.,Design Patterns for Derivatives Software.Vrije University - Amsterdam,2000.
[20]BARONE-ADESI G.,FUSARI N.AND THEAL J.,Barrier Option Pricing Using Adjusted Transition Probabilities,University of Lugano,May 2007.
[21]VETZAL K.R.AND FORSYTH P.A.,Discrete Parisian and delayed barrier options:a general numerical approach,Advances in Futures and Options Research 10,pp.1-15.
[22]DAVIS M.,Mathematics of Financial Markets,Mathematics Unlimited -2001& Beyond.Springer,Berlin,Austrian Science Foundation,2000.
[23]RITCHKEN P.,On Pricing Barrier Options,The Journal of Derivatives,Winter 1995,pp.19-28.
[24]DERMAN E.,KANI I.AND CHRISS N.,Implied Trinomial Trees of the Volatility Smile,Goldman Sachs - Quantitative Strategies Research Notes,February 2006.