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随机利率下股票价格服从指数O-U过程的期权定价
引用本文:李美蓉.随机利率下股票价格服从指数O-U过程的期权定价[J].合肥工业大学学报(自然科学版),2009,32(4).
作者姓名:李美蓉
作者单位:合肥师范学院,数学系,安徽,合肥,230061;合肥工业大学,数学系,安徽,合肥,230009
基金项目:安徽省高等学校省级自然科学重点研究项目,合肥师范学院教学研究项目 
摘    要:文章建立了股票价格服从指数O-U过程的随机微分方程,在风险中性的假设下利用Girsanov定理找到了该模型的唯一等价鞅测度;利用期权定价的鞅方法,得到了随机利率情形下股票价格服从指数O-U过程,并且影响利率的因素与影响股票价格的因素相关时欧式期权的定价.

关 键 词:Ornstein-Uhlenbeck过程  随机利率  Girsanov定理  期权定价

Option pricing with the underlying stock price driven by Ornstein-Uhlenbeck process under stochastic interest rates
LI Mei-rong.Option pricing with the underlying stock price driven by Ornstein-Uhlenbeck process under stochastic interest rates[J].Journal of Hefei University of Technology(Natural Science),2009,32(4).
Authors:LI Mei-rong
Institution:1.Dept.of Mathematics;Hefei Teachers College;Hefei 230061;China;2.Dept.of Mathematics;Hefei University of Technology;Hefei 230009;China
Abstract:The paper constructs the stochastic differential equation of the stock price whose process is driven by the exponential Ornstein-Uhlenbeck process.Under the risk-neutral hypothesis,the equivalent martingale measure is found by means of Girsanov theorem.The European option pricing on stocks is obtained as the price is driven by the exponential Ornstein-Uhlenbeck process under stochastic interest rates and the factors affecting the interest rate and the price of the stocks are correlative.
Keywords:Ornstein-Uhlenbeck process  stochastic interest rate  Girsanov theorem  option pricing  
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