双币种远期契约与双币种障碍期权的定价模型
|
摘要
近年来，随着投资的全球化，双币种衍生证券越来越受到投资者的青睐。它们的收益不仅依赖于某国的标的资产，而且还受到汇率变动的影响，实际收益用另一国的货币表示。根据外国标的资产和汇率，可以构造出许许多多不同的组合。来满足不同投资者和套期保值者的需要。
本文运用风险中性定价理论，求出了随机利率情形下4类双币种远期契约的定价公式以及它们的远期价格。同时，利用鞅方法求出了常利率情形下4类双币种障碍期权的解析表达式，为实践者提供理论上的参考价值。该文组织结构如下：
在第一章中，简要地介绍了本文研究的来源，对象以及所使用的研究方法。
在第二章中，介绍了本文所使用的几个数学定理和一些与本文有关的假设。
在第三章中，首先，将双币种远期契约进行分类，运用风险中性定价理论，推导出了在Hull & white利率模型下，4种双币种远期契约的价格表达式以及它们的远期价格。
在第四章中，将双币种障碍期权分成4类，求出了在常利率情形下4种双币种障碍期权的封闭解。
第五章，总结与展望。
With the growth in globalization of investments in recent years, the quanto derivative securities have gained wider popularity. Their payoffs are determined not only by a financial asset price or index in one currency but also by the exchange rate. The payoffs of these quanto derivative securities can be structured in a variety of combinations of linking foreign asset price and exchange rate, thus generating a rich set of choices of investment and hedging opportunities for investors.
In this paper, according to the Risk-Neutal pricing theory, the four types of quanto forward contracts where the domestic and foreign interest rates are assumed to be stochastic are derived. In the meantime, four closed-formed solutions to quanto barrier options are obtained by making use of the Martingale pricing Method, so series of reference pricing are provided in practice.
This paper is organized as follows:
In chapter 1, we simply introduce the origin, objective and the way used of this paper.
In chapter 2, we simply recalled several mathematics theorem and some supposition relative to this paper.
In chapter 3, Quanto forward contract is classified into four types. Four prices formulas and forward prices for four types of quanto forward contracts where the domestic and foreign interest rate are assumed to be satisfied Hull & White model are derived.
In chapter 4,Quanto barrier option is also classified into four types. Four closed-form solutions to quanto barrier options where the domestic and foreign interest rate are assumed to be constant are obtained by making use of the Martingale pricing Method.
In chapter 5, conclusion and prospects.
本文运用风险中性定价理论，求出了随机利率情形下4类双币种远期契约的定价公式以及它们的远期价格。同时，利用鞅方法求出了常利率情形下4类双币种障碍期权的解析表达式，为实践者提供理论上的参考价值。该文组织结构如下：
在第一章中，简要地介绍了本文研究的来源，对象以及所使用的研究方法。
在第二章中，介绍了本文所使用的几个数学定理和一些与本文有关的假设。
在第三章中，首先，将双币种远期契约进行分类，运用风险中性定价理论，推导出了在Hull & white利率模型下，4种双币种远期契约的价格表达式以及它们的远期价格。
在第四章中，将双币种障碍期权分成4类，求出了在常利率情形下4种双币种障碍期权的封闭解。
第五章，总结与展望。
With the growth in globalization of investments in recent years, the quanto derivative securities have gained wider popularity. Their payoffs are determined not only by a financial asset price or index in one currency but also by the exchange rate. The payoffs of these quanto derivative securities can be structured in a variety of combinations of linking foreign asset price and exchange rate, thus generating a rich set of choices of investment and hedging opportunities for investors.
In this paper, according to the Risk-Neutal pricing theory, the four types of quanto forward contracts where the domestic and foreign interest rates are assumed to be stochastic are derived. In the meantime, four closed-formed solutions to quanto barrier options are obtained by making use of the Martingale pricing Method, so series of reference pricing are provided in practice.
This paper is organized as follows:
In chapter 1, we simply introduce the origin, objective and the way used of this paper.
In chapter 2, we simply recalled several mathematics theorem and some supposition relative to this paper.
In chapter 3, Quanto forward contract is classified into four types. Four prices formulas and forward prices for four types of quanto forward contracts where the domestic and foreign interest rate are assumed to be satisfied Hull & White model are derived.
In chapter 4,Quanto barrier option is also classified into four types. Four closed-form solutions to quanto barrier options where the domestic and foreign interest rate are assumed to be constant are obtained by making use of the Martingale pricing Method.
In chapter 5, conclusion and prospects.
引文
[1] F. Black and M.Scholes(1973),"The pricing of options and Corporate Liabilities", Journal of Political Economy,81,P.637-659.
[2] E.Derman, P. Karasiuski and J. S. Weeker(1990)," understanding Guaranteed Exchange Rate contracts in Foreign stock investments", International Equity strategies, June,Goldman sachs.
[3] J.O.Grabbe,(1983)."The pricing of call and put options on Foreign Exchange", Journal of International Money and Finance,2,P.231-237.
[4] E.Reiner,(1992),"Quanto Mechanics",Risk,March,P.59-63.
[5] J.Z.Wei,"Valuing Derivatives Linked to Foreign Assets", Chapter 5,Fronters in Derivatives ,Edited by A.Konishi and R. Dattatreya,Irwin Professional Publishing(1997).
[6] A.Dravid,M.Richardson,and T.Sun, "Pricing Foreign Index Contingent Claims:An Application to Nikkei Index Warrants", The Journal of Derivatives,Fall 1993,33-51.
[7] K.B.Tofe and E.S.Reiner,"currency-translated foreign equity option: the American case, advances in Futures and option Research,(9)1997,233-264.
[8] Y.K.Kwok and H.Y.Wong,"Currency-translated foreign equity options with path dependent feature and their multi-asset extensions",International Journal of Theoretical and applied to Finance,Vol.3,NO.2(2000).257-278.
[9] J.E.Hilliard,J.Madara and A.L.Tucher,"Currency option pricing with stochostic domestic and foreign interest rates", Journal of Finance and Quantitative Analysis,Vol.26(1991):139-151.
[10] L.J.Wang and S.G.Zhang,"pricing the Asian option under Vasicek interest rate", Acta Mathematical Appli.Sinica(PRC),26(3)2003:467-474.
[11] J.Hull,"Option,Furtures and other Derivatives", Fourth Edition,Prentice-Hall,2000.
[12] R.Heynen and H.Kat,"Crossing the barrier",Pdsk 7(6)(1994)46-51.
[13] H.Johuson,"Option on the maximum or the minimum of seceral assets",J.Financial and Quantitative Analysis 22(1987)277-283.
[14] J.M.Harrison,"Brownian Motion and stochastic Flow systems" ,Wiley, New York,1985.
[15] Steven shreve,"Stochastic Calculus and Finance",October 6.1997.
[16] 陈松男，“金融工程学”，复旦大学出版社，2002年11月，p．175-205．
[17] 洛伦兹．格利茨／著，唐旭等／译，“金融工程学”，修订版，经济科学出版社，1999年11月，p．3-6．
[18] 姜礼尚，“期权定价的数学模型和方法’，高等教育出版社，P．218-222．
[19] [美]斯蒂格利茨，“经济学”，第二版，中国人民大学出版社．
[20] 王雄．姚落根，杨向群，“欧式向上出局看涨认购权证的鞅方法定价”，经济数学，2004年第一期．
[2] E.Derman, P. Karasiuski and J. S. Weeker(1990)," understanding Guaranteed Exchange Rate contracts in Foreign stock investments", International Equity strategies, June,Goldman sachs.
[3] J.O.Grabbe,(1983)."The pricing of call and put options on Foreign Exchange", Journal of International Money and Finance,2,P.231-237.
[4] E.Reiner,(1992),"Quanto Mechanics",Risk,March,P.59-63.
[5] J.Z.Wei,"Valuing Derivatives Linked to Foreign Assets", Chapter 5,Fronters in Derivatives ,Edited by A.Konishi and R. Dattatreya,Irwin Professional Publishing(1997).
[6] A.Dravid,M.Richardson,and T.Sun, "Pricing Foreign Index Contingent Claims:An Application to Nikkei Index Warrants", The Journal of Derivatives,Fall 1993,33-51.
[7] K.B.Tofe and E.S.Reiner,"currency-translated foreign equity option: the American case, advances in Futures and option Research,(9)1997,233-264.
[8] Y.K.Kwok and H.Y.Wong,"Currency-translated foreign equity options with path dependent feature and their multi-asset extensions",International Journal of Theoretical and applied to Finance,Vol.3,NO.2(2000).257-278.
[9] J.E.Hilliard,J.Madara and A.L.Tucher,"Currency option pricing with stochostic domestic and foreign interest rates", Journal of Finance and Quantitative Analysis,Vol.26(1991):139-151.
[10] L.J.Wang and S.G.Zhang,"pricing the Asian option under Vasicek interest rate", Acta Mathematical Appli.Sinica(PRC),26(3)2003:467-474.
[11] J.Hull,"Option,Furtures and other Derivatives", Fourth Edition,Prentice-Hall,2000.
[12] R.Heynen and H.Kat,"Crossing the barrier",Pdsk 7(6)(1994)46-51.
[13] H.Johuson,"Option on the maximum or the minimum of seceral assets",J.Financial and Quantitative Analysis 22(1987)277-283.
[14] J.M.Harrison,"Brownian Motion and stochastic Flow systems" ,Wiley, New York,1985.
[15] Steven shreve,"Stochastic Calculus and Finance",October 6.1997.
[16] 陈松男，“金融工程学”，复旦大学出版社，2002年11月，p．175-205．
[17] 洛伦兹．格利茨／著，唐旭等／译，“金融工程学”，修订版，经济科学出版社，1999年11月，p．3-6．
[18] 姜礼尚，“期权定价的数学模型和方法’，高等教育出版社，P．218-222．
[19] [美]斯蒂格利茨，“经济学”，第二版，中国人民大学出版社．
[20] 王雄．姚落根，杨向群，“欧式向上出局看涨认购权证的鞅方法定价”，经济数学，2004年第一期．