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...

In theory, by trading options, market participants asses and set future volatilities that can be identified using the Black-Scholes-formula in reverse. In reality, as regression analysis suggests, it is historical market data which instead are used to determine future values. Further analysis...