Firm Value Pricing Model for Credit-Risky Claims in Fractional Brownian Motion Environment

Base on the stochastic evolution of the value of the firm's assets, we establish a credit risk model for the valuation of derivatives with counter party default risk in fractional Brownian motion environment, the credit risk is modeled with a firm-value approach. We discuss the credit risk model with the stochastic recovery rate, the explicit pricing formulae for vulnerable call and put options are derived under deterministic interest rate and deterministic firm's liability. In addition, the case of the fixed recovery rate is presented.