期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Pricing of the Maximum or Minimum Option with Uncertain Price
摘要/Abstract
摘要：
研究了随机利率跳扩散环境下具有不确定价格的最值期权定价问题.假设标的资产价格服从跳扩散模型下的多维几何布朗运动，利率服从扩展的Vasicek模型.利用跳扩散模型下的Girsanov定理和测度变换的方法，推导出了具有不确定价格的最值期权的定价公式，从而推广了最值期权的定价模型.
Abstract：
In this paper,we study the pricing of maximum or minimum option with uncertain price under stochastic interest rate and jump diffusion environment.Assuming that the price of underlying assets follows multi-dimensional geometric Brownian motion with jump diffusion model and the interest rate follows the extended Vasicek model,we derive the pricing formula of the maximum or minimum option with uncertain price by using Girsanov's theorem under jump diffusion model and measure transformation.We extend the pricing model of the maximum or minimum option.
关键词
Key words：
option pricing
;
the maximum or minimum option
;
martingale method
;
Vasicek model
参考文献 10
- [1] STULZ R.Options on the Minimum or the Maximum of Two Risky Assets:Analysis and Applications[J].Journal of Financial Economics,1982,6(10):161-185.doi:10.1016/0304-405x(82)90011-3
- [2] MERTON R C.Option Pricing When Underlying Stock Returns Are Discontinuous[J].Journal of Financial Ecomomics,1976,3(1):125-144.doi:10.1016/0304-405X(76)90022-2
- [3] 钱晓松.跳扩散模型中的测度变换与期权定价[J].应用概率统计,2004,20(1):91-99.doi:10.3969/j.issn.1001-4268.2004.01.012 QIAN Xiaosong.Changes of Probability Measure and Options Pricing in Jump-diffusion Models[J].Chinese Journal of Applled Probabitity,2004,20(1):91-99.
- [4] 展瑜萌,李翠香.跳扩散模型下具有信用风险的亚式期权定价[J].辽宁大学学报(自然科学版),2017,44(1):10-14.doi:10.16197/j.cnki.lnunse.2017.01.003 ZHAN Yumeng,LI Cuixiang.Pricing of Asian Options with Default Risks Under Jump-diffusion Models[J].Journal of Liaoning University(Natural Science),2017,44(1):10-14.
- [5] 李艺卓,刘丽霞.跳扩散模型下的二选期权定价[J].宝鸡文理学院学报(自然科学版),2018,38(1):5-9.doi:10.13467/j.cnki.jbuns.2018.01.003 LI Yizhuo,LIU Lixia.The Alternative Option Pricing Under the Jump Diffusion Model[J].Journal of Baoji University of Arts and Sciences(Natural Science),2018,38(1):5-9.
- [6] 李淑锦,李胜宏.随机利率下奇异期权的定价公式[J].数学学报,2008,51(2):299-310.doi:10.3321/j.issn:0583-1431.2008.02.011 LI Shujin,LI Shenghong.Exotic Options Pricing Formulae with Stochastic Interest Rasts[J].Acta Mathematica Sinica,Chinese Series,2008,51(2):299-310.
- [7] 李翠香,石凌.基于随机利率下跳-扩散过程的复合期权定价公式[J].黑龙江大学自然科学学报,2012,29(4):430-436.doi:10.13482/j.issn.1001-7011.2012.04.001 LI Cuixiang,SHI Ling.Pricing Compound Options Under Jump-diffuston Processes with Stochastic Interest Rates[J].Journal of Natural Science of Heilongjiang University,2012,29(4):430-436.
- [8] 薛红.具有不确定执行价格的期权定价模型[J].西安工程科技学院学报,2004,18(1):87-90.doi:10.3969/j.issn.1674-649X.2004.01.019 XUE Hong.Option Pricing Model with Change Exercise Price[J].Journal of Xi'an University of Engineering Science and Technology,2004,18(1):87-90.
- [9] 高新羽,刘丽霞.O-U过程下具有不确定执行价格的领子期权定价[J].西南大学学报(自然科学版),2019,41(7):70-76.doi:10.13718/j.cnki.xdzk.2019.07.010 GAO Xinyu,LIU Lixia.Pricing of Collar Option with Uncertain Strike Price Based on O-U Process[J].Journal of Southwest University(Natural Science),2019,41(7):70-76.
- [10] KLEBANER F C.Introduction to Stochastic Calcus with Applications[M].北京:人民邮电出版社,2008.