Problem And Application Of Default Risk Odels Under Stochastic Liabilities

The main purpose of financial regulation is to maintain economic stability, such as to avoidcrises and sudden adverse changes in the financial system. The core of financial regulationresearch is to measure the default risk. The key study of default risk is to estimate the defaultprobability. The probability of default is the likelihood that a borrower will be unable to repaydebts, sending a loan into default. Now, there are four kinds of the measurement methods ofdefault probability: the method based on the history information of internal credit rating; basedon the measurement of option pricing theory; based on the methods of insurance actuary; basedon the method of risk neutral market. Currently, the studys of default probability rarely considerthe stochastic liabilities. In this dissertation, under the condition of stochastic liabilities, based onthe measurement of option pricing theory, we discuss the explicit solutions of default probabilitywhen the firm value is driven by the jump difusion process. Then assume the default boundaryis a stochastic process. We price the value of the life insurance contracts.First, we discuss the default probability of a firm based on a jump-difusion model, in whichthe asset value of the firm is assumed as the jump-difusion process. The jump-difusion processincludes two cases: the jump part with the logarithm of the jump sizes obey a normal distributionand the jump part with the logarithm of the jump sizes obey a double exponential distribution.By introducing the stochastic barrier, the paper analyzes their respective default probability:(i)For log-normal jump-difusion model, the paper derives the closed form under the assumptionof stochastic default barrier; and furthermore, by extending the barrier to a jump stochasticdefault barrier, the paper gets the closed form of default probability.(ii) For double exponentialjump-difusion model, the paper proposes an algorithm for computing the default probability togeneral model, and derives their closed forms for two simple situations.Further, we extend that the default barrier is driven by another jump-difusion model andthe jump part with the logarithm of the jump sizes followed by a normal distribution. Based onthe above conditions, we get the closed form of default probability.Finally, under the stochastic liabilities we value the life insurance contracts in a constantinterest rate environment.