The asymptotic behavior of the term structure of interest rates

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Long-term interest rates play a crucial role in valuing and hedging fixed income products and derivatives, as well as in pricing future payments for long-term projects or compensatory adjustments in various situations. Following the 2008 financial crisis, the modeling of interest rate curves over extended time horizons gained significance due to increased investments in long-term products. Consequently, understanding the asymptotic behavior of the term structure of interest rates has become increasingly relevant. This research investigates long-term interest rates—specifically, those with infinite maturity—in the post-crisis interest rate market. It explores three concepts: long-term yield, long-term simple rate, and long-term swap rate, analyzing their properties and interrelations. The study particularly focuses on the asymptotic behavior of interest rate term structures within specific models. It computes the three long-term interest rates using the Heath-Jarrow-Morton (HJM) framework with various stochastic drivers, including Brownian motions, Lévy processes, and affine processes on the state space of positive semidefinite symmetric matrices. The HJM framework allows for direct modeling of the entire yield curve. By considering broader classes of drivers, the research accounts for the impact of different risk factors and their interdependencies on the long end of the yield curve. Additionally, it examines long-term interes