Jump-Diffusion models help improve pricing of financial securities by capturing interest rate dynamics accurately. By combining these models with state-dependent volatility, researchers created a class of models that better reflect real-world data. The Heath, Jarrow, and Morton framework is a powerful tool for studying interest rate behavior, allowing for various model possibilities. By adjusting the volatility of forward rates, the model can be simplified to be more computationally manageable. The research also developed Markovian versions of these models, making them easier to work with and apply to different scenarios, such as defaultable term structures.