In this paper, we propose a method to price collateralized debt obligations (CDO) within Merton's structural model on underlyings with a stochastic mean-reverting covariance dependence. There are two key elements in our development, first we reduce dimensionality and complexity using principal component analysis on the assets' covariance matrix. Second, we approximate this continuous multidimensional structure using a tree method. Trinomial-tree models can be developed for both the principal components and the eigenvalues assuming the eigenvectors are constant over time and the eigenvalues are stochastic. Our method allows us to compute the joint default probabilities for k defaults of stochastically correlated underlyings and the value of CDOs in a fast manner, without having lost much accuracy. Furthermore we provide a method based on moments to estimate the parameters of the model.Stochastic covariance matrix, CDO, Trinomial-trees, Principal component analysis, Method of moments,

An early warning system to timely forecast turbulences in the Asian and European stock market is proposed. To ensure comparability, the model is constructed analogously to the early warning system for the US stock market presented by Hauptmann et al. (2014). Based on the time series of discrete monthly returns of the Nikkei 225 and the EuroStoxx 50, filtered probabilities are estimated by two successive Markov-switching models with two regimes each. The market is thus separated in three states: calm, turbulent positive and turbulent negative. Subsequently, a forecasting model using logistic regression and economic input factors is selected. In an empirical asset management case study it is illustrated that the investment performance is improved when considering the signals of the established warning system. Moreover, the US, Asian and European model are compared and interdependencies are highlighted.

Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities with guaranteed minimum repayments at maturity and in case of the insured’s death. If the contract is prematurely surrendered, the policyholder is entitled to the current value of the fund account reduced by the prevailing surrender fee. The financial market and the mortality model are affine linear. For the surrender model, a Cox process is deployed whose intensity is given by a deterministic function (s-curve) with stochastic inputs from the financial market. So, the policyholders’ surrender behavior depends on the performance of the financial market and is stochastic. The presented pricing scheme incorporates the stochastic surrender behavior of the policyholders and is only based on suitable closed-form approximations.