Applying Linear Realization Theory to HJM Markovian Representation

Abstract

Abstract This paper deals with constructing Finite Dimensional Realization (FDR) of HJM with time-invariant hump shape volatility by applying Linear Realization Theory. Two realization algorithms, Standard Observable Canonical Realization and Jordan Canonical Realization, are introduced. The equivalence between Jordan Canonical Realization algorithm and commonly adopted method of constructing FDR is shown by concrete example. At the same time, simulation results indicate that Standard Observable Canonical Realization is better choice for constructing FDR than Jordan Canonical Realization in terms of more precisely capturing the state variables.