Jump-Diffusion models help improve the accuracy of predicting interest rate changes in financial markets. By combining these models with state-dependent volatility specifications, researchers have created a more realistic way to understand interest rate dynamics. The Heath, Jarrow, and Morton framework is a powerful tool for studying interest rates, allowing for the creation of various interest rate models. By making adjustments to the volatility specifications, the framework can be simplified into more manageable Markovian structures. This allows for easier computation while maintaining the flexibility of the original model. The research also explores Markovian versions of defaultable interest rate models, providing insights into how interest rates can be affected by default risks.