Linear-Rational Term Structure Models

Specialeforsvar: Maja Skregeskov Christensen

Titel: Linear-Rational Term Structure Models

Abstract: This thesis investigates Linear-Rational Term Structure Models introduced by Filipovic, Larsson and Trolle in the article ”Linear-Rational Term Structure models” published in 2014.[4] The term structure models give a computational efficiency and
practical method for pricing swaptions. Specifically, the focus is on the Linear-Rational Square-Root (LRSQ) model, which integrates features of the Cox-Ingersoll-Ross (CIR) framework to model interest rate dynamics. This thesis examines the mathematical formulation of CIR and the linearrational framework, extending to multiple variations of the LRSQ model: LRSQ(1,0), LRSQ(1,1), LRSQ(3,1), and LRSQ(3,3). Each variation’s ability to price swaptions and fit empirical data is evaluated through numerical simulations using swap and swaption data from 2019 to 2024. It is seen that models with more parameters like LRSQ(3,1) and LRSQ(3,3) calibrate best to data, while the simpler models LRSQ(1,0) and LRSQ(1,1) do not perform as well. The thesis also assesses the robustness of the LRSQ(3,3) model in capturing the zero lower bound constraints and volatility dependence near this bound. The results demonstrate the flexibility and practical relevance of Linear Rational term structure models for interest rate modeling, providing insights into their semianalytical

Vejleder: David Skovmand
Censor :   David Sloth Pedersen, Danske Bank