Karl Frauendorfer

Management of non-maturing deposits by multistage stochastic programming

Abstract The management of non-maturing account positions in a bank’s balance like savings and sight deposits as well as certain types of variable-rate mortgages is complicated by the embedded options that its clients may exercise. In addition to the usual interest rate risk, uncertainty in the timing and amount of cash flows must be taken into account when investment or refinancing strategies are determined. This paper introduces a multistage stochastic programming model where the stochastic evolution of interest rates and volume under management is described by stochastic processes in discrete time. Scenarios are generated by means of barycentric approximation which is particularly useful to deal with the observed correlations between interest rates and volume. Practical experience from the application at a major Swiss bank is reported where the model has been employed since the mid-90s.

A Stochastic Optimization Model for the Investment of Savings Account Deposits

In a bank’s balance sheet, non-maturing accounts can be characterized as follows: (1) There is no contractual maturity on this kind of account, allowing customers to withdraw or repay their investments or credits at any point in time at no penalty. (2) The customer rate is not indexed to certain interest rates or prices of traded instruments but adjustable to market conditions as a matter of policy. The most common examples include some forms of savings accounts or non-fixed mortgages as they are widespread in Europe and the U.S. These assets and liabilities are not only sensitive to changes in interest rates but have also embedded call or put options that may be excercised by the customer, making their management a particularly ambitious task. A homeowner, e.g., has the option to prepay the outstanding balance of his mortgage and hence, call the security.

Clean Valuation with Regard to EU Emission Trading

In the electric power industry the observed increases of electricity price dynamics combined with the characteristic periodicity of related decision processes have motivated the use of multistage stochastic programming in recent years to provide flexible models for practical applications in the sector. Specifically in power generation and trading the planning process must obey highly complex interrelations between manifold influences. They range from short term price fluctuations as observed in spot markets to long term changes of fundamental influences. Not only changes in the electric supply system itself must be considered, but also the related availability and costs of required fuels. For example, the prices and usability of natural gas in power generation also depend on the existence of respective deployment and distribution systems. Furthermore the electric power sector is exposed to manifold regulatory uncertainties related to the rules imposed by the responsible authorities. Recently environmental issues have become very popular due to the ongoing discussion on climate change. In January 2005 the European Emissions Trading Scheme (EU ETS) has been launched which by many is considered a new key element in efficient electricity market operations. In this paper we will introduce a modeling framework that considers the influence of emission trading on portfolio problems in the electric power sector by applying clean valuation schemes that particularly take fuel costs, emission efficiency in combination with investment possibilities and generation flexibility into account. Sensitivity analysis is performed with respect to changes in technology, volatilities and price scenarios.

Stochastic Optimization in Asset & Liability Management: A Model for Non-Maturing Accounts

A multistage stochastic optimization model for the management of non-maturing account positions like savings deposits and variable-rate mortgages is introduced which takes the risks induced by uncertain future interest rates and customer behavior into account. Stochastic factors are discretized using the barycentric approximation technique. This generates two scenario trees whose associated deterministic equivalent programs provide exact upper and lower bounds to the original problem. Practical experience from the application in a major Swiss bank is reported.