Suchergebnisse

Population forecasts are crucial for many social, political and economic decisions. Official population projections rely in general on deterministic models which use different scenarios for future vital rates to indicate uncertainty. However, this technique shows substantial weak points such as assuming absolute correlations between the demographic components. In this paper, we argue that a stochastic projection alternative, with no a priori assumptions provides point forecasts and probabilistic prediction intervals for demographic parameters in addition. Age-sex specific population forecast for Germany is derived through a stochastic population renewal process using forecasts of mortality, fertility and migration. Time series models with demographic restrictions are used to describe immigration, emigration and time varying indices of mortality and fertility rates. These models are then used in the simulation of future vital rates to obtain age-specific population forecast using the cohort-component method. The consequence for the German pension system is discussed. To maintain the actual average pension level the premium rate of the present system rises at least by 50% as the old-age ratio nearly doubles by 2040.

State price densities (SPDs) are an important element in applied quantitative finance. In a Black-Scholes world they are lognormal distributions but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy no-arbitrage constraints and corrects for the intraday covariance structure in option prices. In contrast to existing methods, we do not use any parametric or smoothness assumptions.