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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. It is a subset of
immunization Immunization, or immunisation, is the process by which an individual's immune system becomes fortified against an infectious agent (known as the immunogen). When this system is exposed to molecules that are foreign to the body, called ''non-s ...
strategies in
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of f ...
. Cash flow matching is of particular importance to
defined benefit pension plans Defined benefit (DB) pension plan is a type of pension plan in which an employer/sponsor promises a specified pension payment, lump-sum, or combination thereof on retirement that depends on an employee's earnings history, tenure of service and ag ...
.


Solution with linear programming

It is possible to solve the simple cash flow matching problem using
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...
. Suppose that we have a choice of j=1,...,n bonds with which to receive cash flows over t=1,...,T time periods in order to cover liabilities L_,...,L_ for each time period. The jth bond in time period t is assumed to have known cash flows F_ and initial price p_. It possible to buy x_ bonds and to run a surplus s_ in a given time period, both of which must be non-negative, and leads to the set of constraints:\begin \sum_^F_x_ - s_ &= L_ \\ \sum_^F_x_ + s_ - s_ &= L_, \quad t = 2,...,T \endOur goal is to minimize the initial cost of purchasing bonds to meet the liabilities in each time period, given by p^x. Together, these requirements give rise to the associated linear programming problem:\min_ \; p^x, \quad \text \; Fx + Rs = L, \; x,s\geq 0where F\in\mathbb^ and R\in\mathbb^, with entries:R_ = -1, \quad R_ = 1In 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

* Cash flow hedging * Debt sculpting * Duration gap * Dedicated portfolio theory *
Fannie Mae The Federal National Mortgage Association (FNMA), commonly known as Fannie Mae, is a United States government-sponsored enterprise (GSE) and, since 1968, a publicly traded company. Founded in 1938 during the Great Depression as part of the N ...
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Immunization (finance) In finance, interest rate immunization is a portfolio management strategy designed to take advantage of the offsetting effects of interest rate risk and reinvestment risk. In theory, immunization can be used to ensure that the value of a portfo ...
*


References

{{Financial_risk Cash flow Corporate finance Derivatives (finance) Financial risk management Linear programming