Finite dimensional Markovian realizations for stochastic volatility forward rate models - Tomas Björk; Camilla Landén; Lars Svensson (Stockholm School of Economics, The Economic Research Institute (EFI), 2002)
We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization theory in order provide general necessary and sufficent conditions for the existence of a finite dimensional Markovian realizations for the stochastic volatility models. We illustrate the theory by analyzing a number of concrete examples.
Keywords: E43; G13; 330; HJM models; stochastic volatility; factor models; forward rates; state space models; Markovian realizations; infinite dimensional SDEs