Assessing the market price of risk in the Hull-White interest rate model

This thesis examines the market price of risk within the Hull-White interest rate model, developing both theoretical foundations and empirical implementation. Through mathematical analysis, we derive explicit formulations for the short rate dynamics under different specifications of the market price of risk, exploring both the constant parameter case \lambda(t) = \lambda_0 and the more state-dependent form \lambda(t) = \lambda_0 + \lambda_1 r(t). Our empirical investigation implements Maximum Likelihood Estimation on historical time series of European yield curves spanning from 2010 to 2024, encompassing various monetary policy regimes. The estimation focuses on the constant market price of risk specification, producing parameters that effectively capture interest rate dynamics across different market environments. The results highlight the significance of incorporating risk premia in interest rate modeling, showing that even a single-factor model with constant market price of risk can explain substantial yield curve variation.