| In this dissertation, we propose a regime switch term structure model built as forward-backward stochastic differential equations. We first generalize the model and study the forward-backward SDEs with discontinuous coefficients. Generally speaking, we adopt the tactics of the Four-Step scheme as our strategy of finding the solution. First, we find a solution v to the PDE associated with the FBSDEs. Then we use this v to decouple the FBSDEs, and solve each equation individually. A weak solution was successfully found. We then returned to the term structure model. We apply the framework of analysis from the general model to the regime switch term structure model, with some minor modifications. A solution, slightly weaker than the general case, was found for the term structure model, as well as the explicit relationship between the short rate and the long term bond price, all of which confirmed our model is fairly well-grounded. Numerical experiments were also conducted to show the validity of our theory. Results are rather satisfactory, providing us with strong empirical support. |
