中文摘要：

假定公司资产价值满足分数布朗运动驱动的随机微分方程,建立了分数布朗运动环境下具有违约风险的未定权益定价模型.运用分数布朗运动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,在利率和公司负债均为常数情形下,获得了脆弱期权定价公式.同时,研究了具有固定回收率的信用风险模型,当固定回收率等于1时,得到了分数布朗运动环境下欧式期权定价公式,推广了分数布朗运动环境下Black-Sholes模型.

英文摘要：

Assume that the value of the firmrs assets satisfies the stochastic differential equation driven by the fractional Brownian motion,the credit risk model is established for the valuation of derivatives with counterparty default risk in fractional Brownian motion environment. Using the stochastic analysis theory of the fractional Brownian motion and the method of actuarial mathematics,the credit risk model is discussed with the stochastic recovery rate,the explicit pricing formulae for vulnerable call and put op- tions are derived under deterministic interest rate and deterministic firm＇s liability. In addition, the case of the fixed recovery rate is presented,when the fixed recovery rate equals 1,the formula is obtained for standard call and put option in fractional Brownian motion environment. It generalizes the Black-Scholes model in fractional Brownian motion environment.