TRINOMIAL-TREE DISTRIBUTION OF A NONLINEAR POSITIVE STOCHASTIC INTEREST RATE MODEL WITH CONNECTIONS TO THE POTENTIAL APPROACH AND ITS APPLICATION TO COMPUTING CORPORATE DEFAULT RISK
Abstract
In this dissertation, I consider a new nonlinear stochastic interest rate model that is adapted from a stochastic population growth model and exhibits the desirable properties of positivity of interest rates and mean reversion. We show that in the constant parameter case this model falls within the paradigm of the Rogers approach for generating positive interest rate models. Moreover, motivated by a procedure initiated by Hull and White, we also oer a variant of the model with a time-dependent parameter that allows calibration of the model to a specified initial term structure when a trinomial-tree method is implemented to obtain discrete approximations of the distributions of the interest-rate process. Although nonlinear, our model has a closed form solution, which facilitates the generation of sample paths by standard numerical methods. This allows us to carry out the trinomial-tree method to obtain approximate distribution of the interest-rate process and compare that result to the approximate distributions obtained by Monte Carlo simulation. We incorporated the positive interest rate to derive the firm's default probability, which thereby extends Qian's work from a linear interest rate model to a non-linear interest rate model. In the research, first comparing to Qian's method, we used the rst passage time method based on the Fortet integral equation to derive the firm's default probability as driven by the Vasicek interest rate model. As an alternative, we also proposed the coupled trinomial tree method to derive the default probability. With the comparison of the numerical results among the three methods, we successfully extended the coupled trinomial tree algorithm for default probability from the linear model to a nonlinear model and obtained reasonably consistent results.
Collections
- OU - Dissertations [9316]
Related items
Showing items related by title, author, creator and subject.
-
Modeling the pecan nut growth and carbohydrate requirement and application of models
Panta, Srijana (2021-12)The pecan nut is an important nut fruit in the USA economy, contributing more than $3.5 billion to the country's economy. The optimal time of different orchard activities like irrigation management, pesticide spray, and ... -
Examining the influences of COVID-19 information avoidance and uncertainty on perceived severity of the pandemic: Applications from the health belief model and Weick’s model of organizing
Chen, Xuewei; Ariati, Jati; Li, Ming; Kreps, Gary (New Prairie Press, 2022-08-30)Public health responses to the COVID-19 pandemic have been insufficient at keeping the virus from spreading rapidly and threatening public health around the globe. Not only has society been challenged by biomedical issues ... -
Modeling futurity: examining epistemological assumptions and political context in urbanization modeling
Snapp, Shelby (2022)Computer simulation models projecting urban expansion are useful for academics, planners, and stakeholders interested in land use patterns and their future implications. Although urban simulation models are being expanded ...