Interbank payment management

Introduction

• Introduction

• Interbank payment management

• Rational cash planning and investment management

• Power production planning

• Supply chain management

• Network stochastic optimization

The aim of stochastic programming is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks and data mining.

• The aim of stochastic programming is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks and data mining.

• Our prime goal is to help to develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.

Active introduction of means of electronic data transfer in banking and concentration of interbank payments were related with creation of an automated system of clearing (ACH).

• Active introduction of means of electronic data transfer in banking and concentration of interbank payments were related with creation of an automated system of clearing (ACH).

• ACH should provide the principles of stability, efficiency, and security. The participants of a system must meet the requirements of liquidity and capital adequacy measures.

• Sensitivity of the sector of interbank payments and settlements to changes makes the subject of investigation on simulation and optimization of interbank payments topical both in theory and in practice.

Nationwide wholesale electronic payments system

• Nationwide wholesale electronic payments system

• Transactions not processed individually

• Banks send transactions to ACH operators

• Batch processing store-and-forward

• Sorted and retransmitted within hours

• Banks

• Originating Depository Financial Institutions (ODFIs)
• Receiving Depository Financial Institutions (RDFIs)

• Daily settlement by RTGS

• Posted to receiver’s account within 1-2 business days

• Typical cost: $0.02 per transaction; fee higher

An overdraft that must be repaid by the close of business the same day

• An overdraft that must be repaid by the close of business the same day

• U.S Federal Reserve allows daylight overdrafts

• Hong Kong does not

Transaction number ID;

• Transaction number ID;

• Sender code a;

• Recipient code b;

• Date and time of transaction t;

• Transaction value P.

The statistical Poisson-lognormal model of electronic settlement flows has been created as well as the methodology for calibrating the settlement flow model has been developed and adapted to the analysis of real time settlement data

• The statistical Poisson-lognormal model of electronic settlement flows has been created as well as the methodology for calibrating the settlement flow model has been developed and adapted to the analysis of real time settlement data

• The methodology of modeling interbank settlement flows by the Monte-Carlo estimator has been developed following to instructions of Central Bank

• The algorithm of stochastic optimization of settlement costs, a view on settlement costs and liquidity risk has been created

Problems of cash management often arise in public, non-profit-making or business institutions

• Problems of cash management often arise in public, non-profit-making or business institutions

• Many companies are faced with choosing a source of short-term funds from a set of financing alternatives

• Various constraints are placed on the financial options. The objective is to minimize the short run financial costs of the financial alternatives plus expected penalty costs for shortages and surpluses in stage’s balances.

Line of credit – is the maximum amount of credit that a financial institution can give out to a business firm. This alternative has two interest rates – one on taken part of the credit line and another on not taken. So, if the firm doesn’t have needs for additional financing, she pays only small interest rate on limit for credit line.

• Line of credit – is the maximum amount of credit that a financial institution can give out to a business firm. This alternative has two interest rates – one on taken part of the credit line and another on not taken. So, if the firm doesn’t have needs for additional financing, she pays only small interest rate on limit for credit line.

Pledging of accounts receivable (factoring) – is the financial transaction whereby a firm may borrow by pledging its accounts receivable to a third part as security for loan. The bank will lend up 70-90% of the face value of pledged accounts receivable and will get remainder 30-10% accounts receivable part then debtor pay all his debt to the bank. For this option firm must pay interest rate for difference from borrowed and reminded parts of the accounts receivable.

• Pledging of accounts receivable (factoring) – is the financial transaction whereby a firm may borrow by pledging its accounts receivable to a third part as security for loan. The bank will lend up 70-90% of the face value of pledged accounts receivable and will get remainder 30-10% accounts receivable part then debtor pay all his debt to the bank. For this option firm must pay interest rate for difference from borrowed and reminded parts of the accounts receivable.

Stretching of accounts payable – the firms, at this option, may delay payments of accounts payable. The firm may stretch up to 80% of the payments due in the period.

• Stretching of accounts payable – the firms, at this option, may delay payments of accounts payable. The firm may stretch up to 80% of the payments due in the period.

• Term loan – the firm may take out a term loan from bank at the beginning of the initial period.

• Marketable securities – the firm may invest any cash in short term securities.

Thus, interpreting financial instruments described above the stochastic linear model for this task is:

• Thus, interpreting financial instruments described above the stochastic linear model for this task is:

• The objective is to minimize the short run financial costs of the financial alternatives plus expected penalty costs for shortages and surpluses in stage’s balances.

The formulation given below refers to a short term financial planning model based on Kallberg, White and Ziemba, 1982.

• The formulation given below refers to a short term financial planning model based on Kallberg, White and Ziemba, 1982.

• Funds are received or disbursed at the beginning of periods.

• All quantities are in thousands of dollars.

• In this model xit – denote the amount obtained from option i in period t, t = 1,2.

Used financial alternatives:

• Used financial alternatives:

• 1 – line of credit (x1t),

• 2 – pledging of accounts receivable (factoring) (x2t),

• 3 – stretching of accounts payable (x3t),

• 4 – term loan (x4),

• 5 – marketable securities (x5t).

• Another used options:

• ARj – accounts receivable, j = 0,1,2. (j – denote planning moments),

• APj – accounts payable,

• LR – liquidity reserve,

• L1 – contribution to liquidity reserve from credit line option,

x6j+, x6j- – surpluses and shortages respectively, j=0,1,2.

• x6j+, x6j- – surpluses and shortages respectively, j=0,1,2.

• r12, r11 – interest rate for taken/not taken part of the credit line,

• r2 – interest rate for pledging of accounts receivable,

• r3 – interest rate for stretching of accounts payable,

• r4 – interest rate for term loan,

• r5 – interest rate for marketable securities,

• rv – norm of cash which can be invested,

• β1 – upper bound of a limit of a credit line,

• β3 – upper bound of stretching of accounts payable,

• β4a , β4v – lower and upper bound of a term loan,

• β41 , β42 – upper bound for constraints on financing combinations,

First stage constraints:

• First stage constraints:

• x11 + L1 ≤ β1 x4 ≤ β4v

• x21 ≥ 0.7 · AR0 x11 + x4 ≤ β41

• x21 ≤ 0.9 · AR0 x21 + x4 ≤ β42

• x31 ≤ 0.8 · AP0 x51 ≤ AR0 ·rv

• x4 ≥ β4a x51 + L1 ≥ LR

• Second stage constraints:

• x12 - L1 ≤ 0 x11 + x12 + x4 ≤ β41

• x22 ≥ 0.7 · AR1 x21 + x22 + x4 ≤ β42

• x22 ≤ 0.9 · AR1 x52 ≤ AR0 ·rv

• x32 ≤ 0.8 · AP1 x51 + x52 + L1 ≥ LR

• x31 + x32 ≤ β3

Initial balance:

• Initial balance:

• First stage balance:

• Second stage balance:

• Objective function:

This model describes the case, when factoring option was used both in first and in the second stages of the financial planning.

• This model describes the case, when factoring option was used both in first and in the second stages of the financial planning.

• Other cases with term loan and factoring options applied or not are similar.

• We analyzed two models. In the first model (TDD) we have used term loan and used factoring option in the first stage, in the second stage we have used or not used factoring option depending on objective function value.

• In the second model (DD) we have not used term loan and have used factoring option in the first stage, in the second stage we have used or not used factoring option depending on objective function value.

The Monte-Carlo method is applied for the solving of the two-stage stochastic model described in (1).

• The Monte-Carlo method is applied for the solving of the two-stage stochastic model described in (1).

• Generated random sample:

• estimator of the objective function is:

• where ,

• sampling variance:

Sampling estimator of the gradient:

• Sampling estimator of the gradient:

• The iterative stochastic procedure of gradient search could be used further: ,

• where is a step-length multiplier, and

• is projection of a gradient estimator to the ε -feasible set.

• Initial solution is obtained solving the deterministic problem.

The approach described above has been realized by means of C++ to solve two-stage stochastic linear model and calculate the objective function by Monte-Carlo method. Two different initial solutions for the subsequent optimization were applied and the software was tested with three data files.

• The approach described above has been realized by means of C++ to solve two-stage stochastic linear model and calculate the objective function by Monte-Carlo method. Two different initial solutions for the subsequent optimization were applied and the software was tested with three data files.

• Results for first (TDD) and second (DD) models are presented below.

Optimal solutions for 3 data sets for TDD model.

• Optimal solutions for 3 data sets for TDD model.

• Optimal solutions for 3 data sets for DD model.

Objective function values during optimization process:

• Objective function values during optimization process:

Optimal objective function values for 3 data sets for TDD model.

• Optimal objective function values for 3 data sets for TDD model.

• Optimal objective function values for 3 data sets for DD model.

Two-stage short term financial planning model under uncertainty was formulated and solved using the Monte-Carlo method for estimation of the objective function.

• Two-stage short term financial planning model under uncertainty was formulated and solved using the Monte-Carlo method for estimation of the objective function.

• The results of computer experiment have been showed that stochastic optimization allows us to compare different financial management decisions.

• Thus, comparison of various alternatives of financial instruments takes opportunities to reduce costs of financial instruments and ensure liquidity as well as optimal planning of the cash flows.

Let the plants are expected to operate over 15 years.

• Let the plants are expected to operate over 15 years.

• The budget for construction of power plants is $10 billion, which is to be allocated for four different types of plants:

• gas turbine,
• coal,
• nuclear power,
• and hydroelectric.

• The objective is to minimize the sum of the investment cost and the expected value of the operating cost over 15 years.

Power plants are priced according to their electric capacity, measured in gigawatts (GW).

• Power plants are priced according to their electric capacity, measured in gigawatts (GW).

• Expected demand for electric power is normally distributed random value D~N(μ, 0.5).

• A set of demands and durations during the year is shown in Table:

Each year costs grow with rate 1%.

• Each year costs grow with rate 1%.

• Since hydroelectric energy depends on the availability of rivers which may be dammed, the geography of the region constrains the hydroelectric power capacity no more than 5.0 GW.

The problem can be modeled as a two-stage stochastic linear optimization model

• The problem can be modeled as a two-stage stochastic linear optimization model

where

• where

The first stage of the problem contains 6 variables and 4 restrictions, the second stage contains correspondingly 375 variables and 375 restrictions.

• The first stage of the problem contains 6 variables and 4 restrictions, the second stage contains correspondingly 375 variables and 375 restrictions.

• Solving the problem the termination conditions have been met after t=123 iterations.

The optimal expected cost of power plant investment problem is turns out to be $16.5030.029 billion versus deterministic cost $17.4750.053 billion.

• The optimal expected cost of power plant investment problem is turns out to be $16.5030.029 billion versus deterministic cost $17.4750.053 billion.

• The size of the last Monte-Carlo sample = 15638, when the total amount of calculations (the size of all Monte-Carlo samples) 290866, thus, the approach developed required only 18.6 times more computations as compared with the computation of one function value.

The approach presented is grounded by the termination and the rule for adaptive regulation of the size of Monte-Carlo samples, taking into account statistical modelling accuracy.

• The approach presented is grounded by the termination and the rule for adaptive regulation of the size of Monte-Carlo samples, taking into account statistical modelling accuracy.

• The proposed termination procedure allows us to test the optimality hypothesis and to evaluate reliably confidence intervals of objective function in a statistical way.

development and operating in supply chain is the critical action of the enterprise

• development and operating in supply chain is the critical action of the enterprise

• the supply network structure (number, location and capacity of facilities) is designed on strategic level

• the amounts of stuffs and goods are planned on operational level

T. Santoso, S. Ahmed, M. Goetschalckx and A. Shapiro. A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 2005, vol. 67, No1, pp. 96-115.

• T. Santoso, S. Ahmed, M. Goetschalckx and A. Shapiro. A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 2005, vol. 67, No1, pp. 96-115.

• S. Wob, and D. L. Woodruf Introduction to Computational Optimization Models for Production Planning in a Supply Chain. Springer, Berlin, 2005.

uncertainty is a critical factor in supply management rising due to globalization

• uncertainty is a critical factor in supply management rising due to globalization

• the disorder of the supply chain causes 8.6% decrease of goods price that can grow up to 20%

• (see, M.Hicks. (2002) When the chain snaps. )

Uncertain factors:

• Uncertain factors:

• investments

• maintenance / transportation costs

• supply

• demand

Supply chain G=(N, A)

• Supply chain G=(N, A)

• N=S ν P ν C – nodes;

• S – suppliers;

• P = M ν F ν W – maintenance points;

• M – production units;

• F – final bases;

• W – warehouses;

• C – customers;

• A = – connections;

Costs of service

• Costs of service

• Response time (delay)

• Throughput

Nonlinear and linear stochastic programming models for application in finance and business have been considered.

• Nonlinear and linear stochastic programming models for application in finance and business have been considered.

• The approach for stochastic optimization by the Monte-Carlo method has been developed

• Computer experiments have been shown that stochastic optimization allows us to compare different managerial decisions.

• Stochastic comparison of various alternatives of managerial decisions takes us opportunities to reduce logistic costs and ensure the reliable meeting of engagements.