Cash flow matching is a process of hedging in which a company or other entity matches its cash outflows (i.e., financial obligations) with its cash inflows over a given time horizon.[1] It is a subset of immunization strategies in finance.[2] Cash flow matching is of particular importance to defined benefit pension plans.[3]

Solution with linear programming

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It is possible to solve the simple cash flow matching problem using linear programming.[4] Suppose that we have a choice of   bonds with which to receive cash flows over   time periods in order to cover liabilities   for each time period. The  th bond in time period   is assumed to have known cash flows   and initial price  . It possible to buy   bonds and to run a surplus   in a given time period, both of which must be non-negative, and leads to the set of constraints: Our goal is to minimize the initial cost of purchasing bonds to meet the liabilities in each time period, given by  . Together, these requirements give rise to the associated linear programming problem: where   and  , with entries: In the instance when fixed income instruments (not necessarily bonds) are used to provide the dedicated cash flows, it is unlikely to be the case that fractional components are available for purchase. Therefore, a more realistic approach to cash flow matching is to employ mixed-integer linear programming to select a discrete number of instruments with which to match liabilities.

See also

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References

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  1. ^ "Cash flow matching". The Washington Post. Archived from the original on November 2, 2012.
  2. ^ "Liability-Driven and Index-Based Strategies". CFA Institute. Retrieved 2020-03-16.[permanent dead link]
  3. ^ "Cash Flow Matching: The Next Phase of Pension Plan Management" (PDF). Goldman Sachs Asset Management. February 2020.
  4. ^ Cornuéjols, Gérard; Peña, Javier; Tütüncü, Reha (2018). Optimization Methods in Finance (2nd ed.). Cambridge, UK: Cambridge University Press. pp. 35–37. ISBN 9781107056749.