Vulnerable Option Pricing In Sub-fractional Brownian Motion Environment

Since1973, Black and Scholes put forward the Black-Scholes option pricing model for the first time and also obtained its pricing formula. In recent years, with the development of the options, it is generally known that credit risk have impact on financial derivatives. 1987, Johnson and Stulz for the first time to analyze the option pricing problem with credit risk, and default option is called vulnerable options. In this research, The pricing problem for vulnerable option is discussed in Sub-fractional Brown motion environment. The dissertation of the paper is organized as follows:(1) We discuss the pricing of vulnerable options in the Sub-fractional Brown environment. Assume that stock price and corporate value obey the stochastic differential equation driven by Sub-fractional Brown motion. The vulnerable option pricing model in Sub-fractional Brown motion environment is established, using the method of actuarial mathematics of Sub-fractional Brownian motion. We discussed the pricing problem of vulnerable option under stochastic liabilities and the pricing formula for vulnerable option is obtained by Sub-fractional Brown motion theory.(2) We discuss the pricing of vulnerable options under fixed liabilities in the Sub-fractional Brown environment. Using the method of actuarial mathematics of Sub-fractional Brownian motion, and get the pricing formula for vulnerable option under fixed liabilities.(3) We discussed the pricing problems of vulnerable options under the Sub-fractional Brown model and jump process. Assume that stock price follows the stochastic differential equation driven by the Sub-fractional Brownian motion and jump process, corporate value obey the stochastic differential equation driven by Sub-fractional Brownian motion. Using the method of actuarial mathematics discussed the pricing problem of vulnerable option under stochastic liabilities and fixed liabilities, The pricing formula for vulnerable option is obtained.