一类杠杆公司的破产概率:回望期权定价方法  

Bankruptcy Probability of a Lever Company:Lookback Option Pricing Met hod

作　　者：杨朝强 田有功 YANG Zhaoqiang;TIAN Yougong(Library,Lanzhou University of Finance and Economics,Lanzhou,730101,China;School of Information Engineering,Lanzhou University of Finance and Economics,Lanzhou,730020,China)

机构地区：[1]兰州财经大学图书馆,兰州730101 [2]兰州财经大学信息工程学院,兰州730020

出　　处：《应用概率统计》2022年第1期1-23,共23页Chinese Journal of Applied Probability and Statistics

基　　金：兰州财经大学科研项目(批准号:Lzufe2019C-009、Lzufe2017C-09);甘肃省高等学校创新基金项目(批准号:2020B-138)资助.

摘　　要：利用结构化方法构造了杠杆公司的金融资产组合,由于公司破产的不可逆性和不确定性,可以把公司破产理解为公司所发行的债券发生违约.通过求解回望期权所满足的抛物型随机偏微分方程,推导出了混合分数跳-扩散模型下杠杆公司的股票定价公式,给出了杠杆公司在财务出现危机时股东通过资本注入来弥补经营损失和清偿债务而没有导致公司破产的概率,同时给出了股东所持有回望期权的定价公式,以及杠杆公司资产的条件分布,从而得到了杠杆公司期权违约概率的显式表达式,最后通过一个算例分析来说明模型的不同Hurst参数及风险系数、股票资产所占权重对杠杆公司破产概率的影响.This paper constructs the assets portfolio of lever corporation by the structural approach.Because irreversibility and uncertainty of corporate bankruptcy, the corporate bankruptcy is equivalent to a default of the bonds. By using the parabolic stochastic partial differential equations(SPDE) which the lookback option satisfied, the assets portfolio pricing model of lever corporation is derived under the mixed jump-diffusion fractional Brownian motion(MJD-fBm) environment. When the lever corporation in the financial crisis, Shareholders use capital injection to make up for operating losses and debt servicing,then the probability of no default before the bonds maturity and the conditional distribution of the lever corporation assets is obtained, and the pricing formula for lookback option is derived. In the end, a numerical example is given to illustrate the influence of different Hurst parameters and risk coefficient and stock asset weight to the default probability of the lever corporation.

关 键 词：结构化方法 回望期权 抛物型随机偏微分方程 混合分数跳-扩散模型 破产概率 

分 类 号：O211.6[理学—概率论与数理统计] F830.91[理学—数学]