Stochastic Dedication: Designing Fixed Income Portfolios Using Massively Parallel Benders Decomposition

Randall S. Hiller and Jonathan Eckstein
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Randall S. Hiller: Delta Global Trading LP, 4 Cambridge Center, Cambridge, Massachusetts 02142
Jonathan Eckstein: Mathematical Sciences Research Group, Thinking Machines Corporation, 245 First Street, Cambridge, Massachusetts 02142

Management Science, 1993, vol. 39, issue 11, 1422-1438

Abstract: Drawing on recent developments in discrete time fixed income options theory, we propose a stochastic programming procedure, which we call stochastic dedication, for managing asset/liability portfolios with interest rate contingent claims. The model uses scenario generation to combine deterministic dedication techniques with stochastic duration matching methods, and provides the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes. We employ a fixed income risk metric that can be interpreted as the fair market value of a collection of interest rate options that eliminates bankruptcy risk from the asset/liability portfolio. We incorporate this metric into a risk/return stochastic optimization model, using a binomial lattice sampling procedure to construct interest rate paths and cash flow streams from an arbitrage-free term structure model. The resulting parametric linear program has a particularly simple subproblem structure, and we have been able to solve it using resource-directed decomposition on a massively parallel computer system, the Connection Machine CM-2. We take a novel approach that uses a standard serial simplex method to solve the master problem, but generates scenarios and Benders cuts in a massively parallel manner. We discuss the performance of this implementation and present the results for a simple pension fund immunization problem.

Keywords: finance; portfolios; stochastic programming; Benders decomposition; computers; parallel; decision analysis; risk (search for similar items in EconPapers)
Date: 1993
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