Michael Schürle

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.

SG-Portfolio Test Problems for Stochastic Multistage Linear Programming

The solvability of dynamic decision problems suffer from the curse of dimensionality which limits the planning horizon one can afford for mapping the real problem into a numeric solvable dynamic optimization model. In this note, stochastic multistage programming is applied to dynamic fixed-income portfolio selection. We report on the goodness fixed income portfolio problems are currently solved with, using barycentric approximation. In particular, it is illustrated how the planning horizon becomes effective with respect to the numerical effort for solving the programs. The computational results serve as benchmark for decomposition methods of mathematical programming.

Term Structure Models in Multistage Stochastic Programming: Estimation and Approximation

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.

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.

Barycentric Bounds in Stochastic Programming : Theory and Application

The design and analysis of efficient approximation schemes are of fundamental importance in stochastic programming research. Bounding approximations are particularly popular for providing strict error bounds that can be made small by using partitioning techniques. In this chapter we develop a powerful bounding method for linear multistage stochastic programs with a generalized nonconvex dependence on the random parameters. Thereby, we establish bounds on the recourse functions as well as compact bounding sets for the optimal decisions. We further demonstrate that our bounding methods facilitate the reliable solution of important real-life decision problems. To this end, we solve a stochastic optimization model for the management of nonmaturing accounts and compare the bounds on maximum profit obtained with different partitioning strategies.

Dynamic Replication of Non-Maturing Assets and Liabilities

Non-maturing assets and liabilities (NoMALs) are those positions in a banks balance that have no contractual maturity such as traditional savings deposits. For the calculation of transfer prices and the quantification of interest rate risk, a fix maturity profile must be assigned to a NoMAL position. Usually a replicating portfolio of fixed-income instruments with constant weights is determined from historical data whose cash flows match those of the underlying position. As an alternative, a multistage stochastic programming model is proposed where the replicating portfolio is derived from representative scenarios of the relevant risk factors (market rates, client rate, volume). Moreover, the portfolio composition is frequently readjusted using the current information about market rates and changes in volume. Compared to the traditional static method, practical experience shows that the margin of NoMALs can be significantly increased at reduced volatility by such a dynamic approach.

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.