Multistage stochastic programming is applied to optimal funding and to multistage mean-variance analysis. Optimal funding is part of the fixed income management where the various types of interest rate risk have to be controlled, primarily. Mean-variance is used within asset allocation for controlling the equity risk, fond manager are exposed to, mainly. Both problems suffer from the curse of dimensionality due to the dynamic decision making. It is discussed, how the funding model and the multistage mean-variance model benefit from the convexity of their value functions with respect to numerical solvability.
The existence of changing correlation structures needs to be taken into account when modelling an asset allocation situation. DEVA + (Dynamic Expectation Variance Analysis) is a multiperiod stochastic optimization approach to identify the optimal tactic and strategic asset allocation. The identified allocation strategies are efficient in a multiperiod context, i.e. under consideration of rebalancing activities, transaction costs, stochastic correlations and volatile financial markets. The dynamic asset allocation approach is designed for financial institutes, which have to fulfil a pension and insurance mandate (DEVA + L, where L stands for liability), and for investors, who want to assess their own asset allocation results against the background of the general market development (DEVA + B, where B stands for benchmark).
This work deals with the approximation of convex stochastic multistage programs allowing prices and demand to be stochastic with compact support. Based on earlier results, sequences of barycentric scenario trees with associated probability trees are derived for minorizing and majorizing the given problem. Error bounds for the optimal policies of the approximate problem and duality analysis with respect to the stochastic data determine the scenarios which improve the approximation. Convergence of the approximate solutions is proven under the stated assumptions. Preliminary computational results are outlined.
Über Herausforderungen und Potentiale im ALM heute, das Konzept der stochastischen Optimierung und die gewonnenen Erfahrungen innerhalb einer Kooperation mit einer schweizerischen Grossbank.
A bank's financial management faces various sources of uncertainty when funds from savings account deposits are invested in the marketplace. Future interest rates are unknown and customers are allowed to withdraw their deposits at any point in time. The objective is to find a portfolio of fixed income instruments that maximizes the bank's interest surplus from the investment of funds and to manage the prepayment risk inherent to non-maturing accounts. A multistage stochastic programming model is presented that takes into account the uncertain evolution of interest rates and volume. A case study based on interest rate data of a 7 years period indicates that the surplus can be increased by 25 basis points compared to the static approach formerly used, while volatility is reduced significantly.
This paper analyzes the reaction of the S&P 500 returns to changes in implied volatility given by the VIX index, using a daily data sample from 1990 to 2012. We found that in normal regimes increases (declines) in the expected market volatility result in lower (higher) subsequent stock market returns. Thus, investors enter into selling positions upon a perception of increased risk for their equity investments, while they enter into long positions when they perceive an improved environment for those investments. However, for extreme regimes investors' reaction to increasing risk is ambiguous. We found that VIX variation significantly influences investment strategies for holding periods up to one month. Additionally we propose an investment rule for short-term oriented investors.
