Optimization of Constrained Liquidity Management

Abstract

A consistent framework for optimal liquidity management is presented. This framework optimizes the cost of covering expected cashflow gaps without violating regulatory and business constraints. Anticipated economic value loss, cashflow loss, and adverse market impact are the major drivers of cost. The notion of a deployable liquidity resource, which is subsequently extend to the notion of a dated liquidity strategy, is introduced. A formalization of LCR as a typical regulatory constraints is presented and included in the formulation. The formulation includes a general arbitrage free market impact function. A decoupling between liquidity risk management and that of market and credit risks is assumed. Both linear and quadratic programming approaches for solving the resulting optimization problem are derived. This is followed by the introduction of a novel mapping algorithm which transforms the linear program to a network flow problem that is more efficiently solvable via the network simplex algorithm. Next an algorithm for generating a plausible starting point for the iterative optimization problem, is given. This is shown to be already optimal under the risk neutral measure. Finally, heuristics that can help speed up the satisfaction of regulatory constraints are discussed. Throughout the presentation attention is given to algorithmic complexity issues.