State price density models for the term structure of interest rates: Applications to insurance and expansions to the stock market and macroeconomic variables

We consider two term structure models for long-term insurance applications within the state-price-density-framework of Rogers (1997): the Cairns (2004) model and the new cosh model. Both are estimated by the Extended Kalman Filter and analyzed for long-term dynamics and historical fit. Two expansions to stock market dynamics, one based on the Black-Scholes stock market model and one based on discounted dividends are presented. Finally, an expansion to macroeconomic data is discussed.