多跳-扩散模型与脆弱欧式期权定价  

Multiple Jumps-Diffusion Model and Vulnerable European Option Pricing

作　　者：魏正元[1] 高红霞[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《应用概率统计》2011年第3期232-240,共9页Chinese Journal of Applied Probability and Statistics

基　　金：重庆市教委科学技术研究项目基金(KJ100819)资助

摘　　要：本文对期权的标的资产价格和合约空头方的资产-债务比(Assets-to-Liabilities)引入有多个跳风险源的跳-扩散过程(Jump-Diffusion Process)进行建模.用几何Brown运动描述其常态连续运动的情形,用多个不同强度的Poisson过程描述遭受各种新信息或稀有偶发事件所触发的各种跳发生的记数过程,用多个不同的对数正态随机变量描述各种跳所对应的跳幅度,并假定跳风险是可分散的.在模型限定下,我们应用It引理和等价鞅测度变换,导出了公司价值型信用风险欧式期权一般化的封闭形式的解析定价公式,推广了经典的结构信用风险期权定价以及状态变量带单跳的跳-扩散情形,同时也从定量的角度完善了Zhou(2001)和Lobo(1999)的工作.A mixed diffusion process involving various sources of jumps is introduced to characterize both the price of underlying asset and the ratio of firm＇s assets to liabilities.Continuous component is modeled as geometric Brownian motion to describe their ＂normal＂ revolution,and discontinuous component is modeled as jumps with several Poisson arrival processes in conjunction with corresponding random jump size to characterize their sudden increase or drop in a surprising manner instantaneously.This may be due in part to the impact of rare events and new information,such as technological innovation,regulatory effects,catastrophic rare events and so on...These jumps are assumed independent of each other,with each type having a log-normally distributed jump size,we also supposed that all jumps risk is diversifiable and hence not priced in equilibrium.By applying It lemma and equivalent martingale measure transformation within the framework of our model,we derived a closed form of analytic solution for vulnerable European option,and therefore generalized classical formula for vulnerable European option with jump and quantified the works by Zhou（2001） and Lobo（1999）.

关 键 词：多跳-扩散过程 信用风险 脆弱欧式期权 期权定价 

分 类 号：O21[理学—概率论与数理统计] F830.9[理学—数学]