On the construction of finite dimensional realizations for nonlinear forward rate models (Q1409832)

Heath-Jarrow-Morton type interest rate models are considered in which the forward rates are driven by a multidimensional Wiener process and the volatility structure is a smooth functional of the present forward rate curve. A general method of finite-dimensional Markovian state space realization (FDR) construction is described. The method is illustrated by the construction of FDR for deterministic direction volatilities model of the form \(\sigma(r,x)=\varphi(r)\lambda(x)\) or \(\sigma(r,t,x)= \sum\varphi_j(r,t)\lambda_j(t,x)\) for time varying systems.