Inference of Term Structure Models

Compared with deterministic models, the key feature of a stochastic differential equation (SDE) model is its ability to generate a large number of different trajectories. To tackle the challenge, a number of methods have been proposed to infer reliable estimates. But these methods dominantly used the explicit methods for solving SDEs, and thus are not appropriate to deal with experimental data with large variations. In this work we develop a new method by using implicit methods to solve SDEs, which is aimed at generating stable simulations for stiff SDE models. The particle swarm optimization method is used as an efficient searching method to explore the optimal estimate in the complex parameter space. Using the interest term structure model as the test system, numerical results showed that the proposed new method is an effective approach for generating reliable estimates of unknown parameters in SDE models.