非对称双指数跳扩散模型下重置期权的定价
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摘要
在非对称双指数跳扩散模型下运用概率方法导出了重置期权的价格公式。首先引入非对称双指数跳扩散模型并详尽分析了它的特点。其次,在经Girsanov定理进行测度变换的基础上利用Brownian运动和Poisson分布的独立增量性及Markovian性将期权价格转化为一些易于计算的数学期望之和。最后利用全期望公式给出重置期权明确的价格计算公式。
In this paper,aprobabilistic method is applied to get the formulas of reset options in asymmetric double exponential jump-diffusion models.Firstly,a asymmetric double exponential jump-diffusion model is introduced and the characteristic of the models is discussed.Secondly,through the change of measure based on Girsanov's theorem and by the properties of Markovian and independent increments for Brownian motions and Poisson processes,the price can be computed as the sum of some expectations which are relatively to calculate.Furthermore,by total expectation formula,the explicit pricing formula for reset options is provided.
In this paper,aprobabilistic method is applied to get the formulas of reset options in asymmetric double exponential jump-diffusion models.Firstly,a asymmetric double exponential jump-diffusion model is introduced and the characteristic of the models is discussed.Secondly,through the change of measure based on Girsanov's theorem and by the properties of Markovian and independent increments for Brownian motions and Poisson processes,the price can be computed as the sum of some expectations which are relatively to calculate.Furthermore,by total expectation formula,the explicit pricing formula for reset options is provided.
引文
[1]李松芹,张寄洲.跳扩散模型下重置期权的定价[J].高等学校计算数学学报,2005,27(12):182-187.
[2]李红,邓国和,杨向群.跳跃扩散模型外汇重置期权定价[J].福州大学学报(自然科学版),2006,34(1):28-31.
[3]王莉君,张曙光.随机利率下重置期权的定价问题[J].高校应用数学学报,2002,17(4):471478.
[4]石伟,刘丽霞.基于多个资产几何平均值的重置期权的定价[J].周口师范学院学报,2016,33(2):4-10.
[5]郭尊光,李灿,仉志余.基于辛普森公式的美式期权定价最优实施边界新算法[J].南昌大学学报(理科版),2015,39(6):525-528.
[6] MERTON R.Option Pricing When Underlying Stock Returns are Discontinuous[J].Journal of Financial Economics,1976,3(1-2):125-144.
[7] KOU S G.A Jump-diffusion Model for Option Pricing[J].Management Science,2002,48(8):1086-1101.
[8] RUNGGALDIER W J.Jump-diffusion Models[A].Rachev,S T Hand book of heavy Tailed Distributions in Finance[C].Elesevier:North-Holland,2003:169-209.
[9] PROTTER P.Stochastic Integration and Differential Equations[M].Berlin:Springer,1990.
[2]李红,邓国和,杨向群.跳跃扩散模型外汇重置期权定价[J].福州大学学报(自然科学版),2006,34(1):28-31.
[3]王莉君,张曙光.随机利率下重置期权的定价问题[J].高校应用数学学报,2002,17(4):471478.
[4]石伟,刘丽霞.基于多个资产几何平均值的重置期权的定价[J].周口师范学院学报,2016,33(2):4-10.
[5]郭尊光,李灿,仉志余.基于辛普森公式的美式期权定价最优实施边界新算法[J].南昌大学学报(理科版),2015,39(6):525-528.
[6] MERTON R.Option Pricing When Underlying Stock Returns are Discontinuous[J].Journal of Financial Economics,1976,3(1-2):125-144.
[7] KOU S G.A Jump-diffusion Model for Option Pricing[J].Management Science,2002,48(8):1086-1101.
[8] RUNGGALDIER W J.Jump-diffusion Models[A].Rachev,S T Hand book of heavy Tailed Distributions in Finance[C].Elesevier:North-Holland,2003:169-209.
[9] PROTTER P.Stochastic Integration and Differential Equations[M].Berlin:Springer,1990.