Bankruptcy Probability of a Lever Company: Lookback Option Pricing Method

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.