Multi-factor modelling of the term structured financial instruments

<p dir="ltr">Term structure analysis is crucial in modelling financial instruments, as evidenced by the inverted yield curve being a reliable indicator of the approaching economic recession. Understanding the factors influencing adverse market movements is therefore vital for both researchers and practitioners. This thesis focusses on the modelling of the term structure of commodity futures and bond yields, extending existing models in these markets from various perspectives.</p><p dir="ltr">The first study examines the term structure modelling of commodity futures. We introduce a family of stochastic models using polynomial diffusion to estimate the unobservable spot price, which is essential for modelling futures curve dynamics. This framework incorporates a range of non-linear, higher-order effects into a multi-factor model, generalising the classic Schwartz and Smith two-factor model. We employ the Extended Kalman Filter and the Unscented Kalman Filter for parameter and latent factor estimation to address the non-linearity inherent in these models. A comparative analysis of these estimation procedures is provided, and while we identify challenges related to parameter identification in the polynomial diffusion model, accurate futures price estimation remains achievable. Additionally, we explore the impact of different methods for calculating matrix exponentials within this model.</p><p dir="ltr">The second study contributes to statistical software development by introducing the R package “PDSim” to simulate commodity futures prices using the polynomial diffu- sion model presented in the previous study. PDSim enables data simulation through both a Shiny web application and R scripts, providing state variable and contract estimations via the Extended Kalman Filter and the Unscented Kalman Filter. Its user-friendly interface makes these simulation and estimation features accessible to a broad audience. Currently, it is the only package specifically designed for the sim- ulation and estimation of the polynomial diffusion model, and it also integrates the Schwartz and Smith two-factor model as an alternative approach.</p><p dir="ltr">The third study focusses on bond markets. We introduce a novel state-space func- tional regression model that integrates both the dynamic Nelson-Siegel model and functional regression in a multi-economy context. This framework provides distinct advantages in explaining the relative yield spreads between a reference and a response economy. To overcome the challenges of model calibration, a kernel principal com- ponent analysis is employed to transform the functional regression component into a finite-dimensional estimation problem. A comprehensive empirical analysis of eight economies, seven response economies and one reference economy, demonstrates the su- perior in-sample estimation accuracy of the functional regression model compared to the dynamic Nelson-Siegel model. Furthermore, we apply this functional regression model in a stress testing analysis and a bond ladder portfolio case study to illustrate interdependencies between economies and assess potential risks under extreme market conditions.</p>