Karl Frauendorfer
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Prof. Dr.
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Frauendorfer
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Karl
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karl.frauendorfer@unisg.ch
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+41 71 224 2105
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Management of non-maturing deposits by multistage stochastic programming

2003-12-16 , Frauendorfer, Karl , Schürle, Michael

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.

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SG-Portfolio Test Problems for Stochastic Multistage Linear Programming

1995-09-13 , Frauendorfer, Karl , Härtel, Frank , Reiff, Michael F. , Schürle, Michael

The solvability of dynamic decision problems suffers from the curse of dimensionality, which limits the planning horizon one can afford for mapping the real problem into a numerically solvable dynamic optimization model. In this note, stochastic multistage programming is applied to dynamic fixed-income portfolio selection. We report how well some fixed income portfolio problems are currently solved with barycentric approximation. In particular, we illustrate how the planning horizon affects the numerical effort required to solve the programs. The computational results serve as a benchmark for decomposition methods of mathematical programming.

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

2001 , Frauendorfer, Karl , Schürle, Michael , Ziemba, W.T. , Mulvey, J.M.

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Term Structure Models in Multistage Stochastic Programming: Estimation and Approximation

2000-12-01 , Frauendorfer, Karl , Schürle, Michael

This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data for the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.

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Refinancing Mortgages in Switzerland

2005 , Frauendorfer, Karl , Schürle, Michael

This paper presents a multistage stochastic programming model for refinancing mortgages with non-contractual maturity under liquidity restrictions in the market. An extension to the management of other products such as savings accounts is straightforward. The evolution of interest rates is modelled by principal components for short-term and a two-factor mean reversion model with long rate and spread for long-term planning. Barycentric approximation provides tight lower and upper bounds for the original problem with relative discretization errors in the order of one per cent.

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Barycentric Approximation of Stochastic Interest Rate Processes

1998 , Frauendorfer, Karl , Schürle, Michael , Mulvey, J.M. , Ziemba, W.T.

The incorporation of single-factor interest rate models within the stochastic programming methodology is investigated and applied to multiperiod investment. Barycentric approximation is used for discretizing the stochastic factors and for generating scenario trees which take the various term structure movements into account. It is shown that employing the Vasicek model for the instantaneous rate process preserves convexity of the stochastic multistage program and, hence, guarantees information on the accuracy of the approximate investment strategies. To the contrary, the convexity of the program cannot be assessed if the square root process due to Cox-Ingersoll-Ross is used for the instantaneous rate. In this case, the approximate investment policies and their associated interest surplus may be accepted as estimates. Numerical results for 8-period and 6-period investment problems are discussed.

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A Stochastic Optimization Model for the Investment of Savings Account Deposits

1997-09-03 , Forrest, Bruce , Frauendorfer, Karl , Schürle, Michael

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.

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Multistage stochastic programming: Barycentric approximation

2001 , Frauendorfer, Karl , Schürle, Michael , Parkalos, P. , Floudas, C. A.

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