Calibration of Interest Rate Models

The technical paper discusses the calibration of various interest rate models, focusing on one-factor and two-factor models by Hull & White, as well as the Black Karasinski model.

Each model incorporates a deterministic drift, mean reversion speed, and volatility, formulated through stochastic differential equations. The models aim to match the current term structure of interest rates and calibrate to cap and swaption data. Given the ill-posed nature of the problem, the paper emphasizes the use of regularization techniques to stabilize the solutions. These include Tikhonov regularization and iterative methods such as Landweber iteration.

The calibration process involves identifying parameter functions from market data, with the models implemented within the UnRısk framework, providing analytic solutions and stability in pricing various financial instruments.