基于分数维Ho-Lee随机利率模型的具有违约风险的期权定价  

Option pricing under default risk based on fractional Ho-Lee stochastic interest rate model

作　　者：王伟[1] 黄文礼[1,2] 李胜宏[3] 

机构地区：[1]浙江科技学院数学系,浙江杭州310023 [2]中国科学技术大学统计与金融系,安徽合肥230026 [3]浙江大学数学系现代金融研究室,浙江杭州310027

出　　处：《高校应用数学学报（A辑）》2013年第4期406-416,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：中国博士后基金资助;教育部科学技术研究重大项目(309018);国家自然科学基金(70973104;11171304);浙江省自然科学基金(Y6110023)

摘　　要：假设公司资产价值和标的资产价格都满足分数布朗运动驱动的随机微分方程,利率是服从分数维Ho-Lee模型的随机过程,建立了分数布朗运动环境中基于随机利率模型的具有违约风险的欧式看涨期权定价模型.运用分数布朗运动的随机分析理论和保险精算方法,讨论了具有随机回收率的信用风险模型,在公司负债为常数的情形下,利用分数维Ho-Lee随机利率,获得了欧式脆弱期权定价公式.On the hypothesis of the company＇s asset and underlying asset price following the stochastic differential equation driven by fractional Brownian motion, and interest rate being a stochastic process obeying the fractional Ho-Lee model, the pricing model for European call option considering default risk based on stochastic interest rate model in fractional Brownian motion setting is established. The credit risk model with stochastic recovery rate is discussed by using the stochastic analysis theory of the fractional Brownian motion and the actuarial approach. Under the assumption of the company＇s liability being a constant, by applying the fractional Ho-Lee stochastic interest rate, the vulnerable European option pricing formula is obtained.

关 键 词：违约风险 分数布朗运动 分数维Ho—Lee模型 精算方法 期权定价 回收率 

分 类 号：O211.63[理学—概率论与数理统计] F224.7[理学—数学]