THE NON - STOCK EXCHANGE DEALS OPTIMIZATION USING NETFLOW METHOD. V.B.Gorsky, V.P.Stepanov. Saving Bank of Russian Federation,

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1 THE NON - STOCK EXCHANGE DEALS OPTIMIZATION USING NETFLOW METHOD. V.B.Gorsky, V.P.Stepanov. Saving Bank of Russian Federation, dwhome@sbrf.ru Abstract. We would like to present the solution of the following problem: some organization has a number of clients, which have their own portfolios of bonds ( or it can be any type of commodities ). Sometimes they would like to buy, to sell, or to sell one type of bond and to buy another bond on money from the bond sale, or from some client account. The clients can do it through external organizatio(p.e. on Stock Exchange), but the exchange operations between them inside the organization will be more profitable for them. The tasks are 1) to reveal the chains of mutual exchanges between client bids with maximum value of internal bond flow ; 2) to calculate the required external stock exchange operations and the importance of each of them. Each client has its own position in scale of priority. Besides each client has own requisitions on the exchange operation, the price of commodity in sale must be higher then some value and vice versa in buy operations the price must be lower then another value. For example, the 1-st client wants to sell monitors, the 2-nd client wants to sell printers and on received money to buy monitors, the 3-rd client sells keyboards and buys printers, the 4-th client buys keyboards. Some part of client bids can be realized without stock using this chain provided sell and buy prices satisfy each other. But, par example, if the sell price of 3-rd client is higher then buy price of the 4-th client the whole exchange chain will be impossible. It will possible only if some stock buy offer fulfilling the 3-rd client sell requisitions will be found. Besides, in cash flow the whole buy sum must be less then whole sell sum plus client account sum for each client. The resolving algorithm and program find not only horizontal, but also vertical chain exchanges, because the same client can simultaneously buy and sell several commodities. The algorithm finds the required stock exchanges and calculates the order of priority of each of them. The priority of each stock deals is proportional to the number of non-stock exchanges which will be possible after such stock deal completion. The integer-valued solution is founded using iterative netflow algorithm taking into account the whole net of commodity and cash flow, including the cash flows arising due to buy and sell sum mismatch. The primary requests and the final results, including a set of checks, can be in any form: text or excel file, any database format with SAS access. Using netdraw procedure we present the graphical form of obtained solution. The system enables to store and to reproduce the initial conditions and final and intermediate results of obtained resolution in SAS or external database. 1/8

2 THE NON - STOCK EXCHANGE DEALS OPTIMIZATION USING NETFLOW METHOD. V.B.Gorsky, V.P.Stepanov. Saving Bank of Russian Federation, oriscb@sbrf.ru We would like to present our solution of the optimization problem of non-stock exchange deals between and more clients wishful to buy, to sell or to do buy and sell simultaneously some commodities. For example, some organization has a number of clients, which have their own portfolios of bonds. Sometimes they would like to buy, to sell on money from their own account, or to sell one type of bond and to buy another bond on money from the bond sale during the stock-exchange session. The clients can do it through some external organization ( p.e. on Stock Exchange), but direct exchange operations between them without stock exchange will be more profitable for them because of the more acceptable price and absence of stock tax. The resolving of the problem can be subdivided into two stages. - Non-stock exchange decision. The chains of mutual exchanges between the clients with maximum value of internal bond price flow to be revealed. It means that the beginning of all chains are the clients selling the bonds (commodities) and the closing elements of all chains are clients buying bonds (commodities). Insight the chains are clients buying and selling bonds (commodities) simultaneously. Of course every client can have a lot of exchange operations with other clients, even for single bond (or type of commodity). Any connection with external organization (stock exchange) on this stage are prohibited. This deals are to be accomplished before the stockexchange session will begin. - Exchange decision with stock operations. The calculation of the required stock exchange operations and the importance of each of them are to be performed. The importance of any stock exchange operations is defined by the volume of non-stock exchange deals be enabled by the stock operation. We should have an opportunity during the stock session to estimate the losses which we would have if some necessary stock operation would not be accomplished. Additional restrictions. Each client has its own position in scale of priority. In other equal conditions the client with higher priority will be the first in queue on nonstock exchange operations. Besides each client has own requisitions on the exchange operation, the price of commodity in sale must be higher then some value and vice versa in buy operations the price must be lower then some another value. For example, the 1-st client wants to sell monitors, the 2-nd client wants to sell printers and on received money to buy monitors, the 3-rd client sells keyboards and buys printers, the 4-th client buys keyboards. The flow of commodities and cash on each step are defined by the least bid in money terms of exchanges in this chain. Some part of client bids can be realized without stock using this chain provided sell 2/8

3 and buy prices satisfy each other. This is the simplest example of the first non-stock exchange decision. But if we propose that the asked sell price of 3-rd client on keyboards is higher then bid buy price of the 4-th client the whole exchange chain would be impossible. It will be possible only if some stock buy offer fulfilling the 3-rd client asked sell requisitions will be found. In this case we shell obtain internal exchange decision with some stock-end deals. Of course for 4-th client we should found the stock exchange sell offer, with sell price lower than bid buy price of the 4-th client. Some another restrictions exists on commodity quantity flow. For sell deals the maximum sell value is defined by client bid. For buy operation the maximum buy quantity is defined as the least quantity between two values : a) client bid and b) money on client account plus possible client sell operations in money terms. The primary client bids can be read from some standard MS Excel form, or from any relational database with supported SAS connection. The bids include the client code, bid type (sell, buy, or sell and buy), requirements (the acceptable price range), asked bid quantity and money sum on client accounts. Besides some additional information is required, for example average commodity stock prices, because the non-stock exchange operations can be accomplished by average stock prices. Lets consider the stages of the problem solution. 1. We select bids which can take part in non-stock exchange deals. We select clients bids on commodities which are simultaneously in sell and buy bids. Furthermore we select only clients buy bids with prices which are higher then the lowest sell price on the bid commodity, and we select sell bids with prices which are lower then the highest buy price on the bid commodity. 2. The non-selected bids that can be realized only through the stock, because declared commodities are only in sell or only in buy bids, aren t considered in our task later. 3. The non-stock exchange decision is founded. The whole list of exchange operations between clients are calculated. Several checks are to be fulfilled for testing of decision correctness. 4. Exchange decision with stock operations is founded. The list of all required stock deals and non-stock exchange operations available after completion of the stock deals are calculated. Besides the list of non-stock exchange operation is furnished for each required stock deal. In the list opposite to every stock deal the exchange operations are reported which would be impossible if the stock deals will not be accomplished. 3/8

4 Sell Clients Sell Bonds Buy Bonds Buy Clients Client1 Bond1 Bond11 Bond12 Client11 -Money Client2 Bond2 Bond13 Client12 +Money Bond3 Bond14 Client3 Bond4 Bond15 Client13 Fig.1.. The simple sell bids (left) and the buy bids(right). Arrows shows the motion direction of the bonds. Now we shell discuss the items of the non-stock exchange decision in details. 1. We shell use NETFLOW procedure and we shell describe nodes and flow capacities. 2. At first we shell describe simple sell or buy bids. In the NETFLOW PROC this deals are described as in Fig.1. All ARC capacities are expressed in money units. The ARC capacities from - /+MONEY to Clients are INFINITY, while the ARC capacities from CLIENTS to BONDS are (client bids quantity)*(bonds market price). 3. The sell and buy bids are described as in Fig.2. Buy Bonds Bond11 Bond3 Buy and Sell Clients Client21 Sell Bonds Bond1 Bond11 Buy and Sell Clients Client21 Bond1 Bond13 Client22 Bond2 Bond13 Client22 Bond2 Bond14 Bond1 Client23 Bond3 Bond4 Bond14 Client23 Bond3 Bond4 Fig.2. The buy and sell primary bids (left), the scheme after the reducing of the buy and sell bids. Summing up lets enumerate the steps of the net construction for NETFLOW proc. The scheme is shown in Fig.3. 4/8

5 1. We put two nodes -MONEY, +MONEY, which will be the source and the sink nodes. 2. We put all the clients as a nodes on the scheme. 3. We put all the bonds as a nodes taking part in sell and buy bids simultaneously on the scheme. 4. We connect -MONEY with CLIENTs only selling bonds by ARCs with capacities equals to infinity and COST equals to We connect CLIENTs only buying bonds with +MONEY by ARCs with capacities equals to amount of money on clients accounts and COST equals to We connect CLIENTs (nodes), selling bonds, with appropriate SELL BONDs (nodes) with ARCs having capacities equal to (clients sell bids quantity) times (bond market price) and COST equals to We connect CLIENTs (nodes) with +MONEY (nodes) by ARCs having capacities equals to amounts on clients accounts and COST equals to We connect BUY BONDs (nodes) with appropriate CLIENTs (nodes), buying this bonds, by ARCs having capacities equals to (amounts on clients accounts) + (selling bonds sum). All this value is rounded to the price of integer number of buying bonds. COST equals to We connect -MONEY with CLIENTs, both buying and selling bonds, by ARCs taking into account the effect integer rounding, arising due to price difference of selling and buying bonds. The CAPACITY of this ARCs equals to price of appropriate single selling bond, and COST equals to 10. (9) (7) -Money(1) (4) Selling (6) Selling & Buying Buying (5) +Money(1) (8) (6) Bonds(3) (8) Fig.3. The scheme of NETFLOW proc used for problem resolution. Numbers denotes stages described above. Arrows show the bond movement directions< while cash moves in opposite direction. 5/8

6 Now lets consider the algorithm of resolving the NETFLOW proc. Some complication exists: we should obtain the resolution in integer values. Besides the rest from rounding we should include in goal function in some cases. 1) (OUTER LOOP) 2) (INNER LOOP)We resolve the NETFLOW proc. 3) (INNER LOOP)We round the cash flows on arrows with numbers (6) and (8) and limit the CAPAC values on this ARCs with this rounded values. 4) (INNER LOOP)We return to step 1 until the loop convergence. 5) (OUTER LOOP) We decrease the CAPAC values on arrows (6), (7) and (8) on obtained FLOW values. 6) (OUTER LOOP) We increase money client account sums on rounding values: CAPAC of arrows(7) on FLOWS of arrows(9) 7) (OUTER LOOP) Return to step 1 until the values on steps (6) & (8) will be less then the price of appropriate single bond. 8) The final result is the sum of solutions obtained in OUTER CYCLE. The results are represented in table and graph form using NETDRAW proc. Fig.4. Some part of the graphical solution of the NETFLOW proc. Several pages are necessary for representing the all scheme. Each rectangle with clients includes whole information about deals: quantity, bond price, client code; the bond rectangle includes information about the bond.. Now lets consider the second solution : exchange decision with stock operations. The scheme for NETFLOW proc has the following structure (Fig.5). In addition to 9 points shown on Fig.3 and enumerated above for no non-stock exchange operations the following nodes and arcs are added to the scheme. 10. Bonds (nodes), which are only in buy bids, but only for clients having both buy and sell bids, and for which their sell side can take part in non-stock 6/8

7 exchange. For clients buying bonds, which are only in buy bids only stock exchange deal is possible. 11. Bonds (nodes), which are only in sell bids, but for clients having buy side also, that can participate in non-stock exchange STOCK, which is intermediate node between -MONEY and bonds, which are only in buy bids STOCK, which is intermediate node between bonds, which are only in sell bids, and +MONEY. 14. The ARCs between -STOCK and -MONEY, +STOCK and +MONEY have CAPAC equals to INFINITY and COST equals to The ARCs from -STOCK to buy BONDs nodes and from sell BONDs nodes to +STOCK have CAPAC equals to buy and sell bond bids respectively in money terms. The stages of resolution of the scheme are the same as it was discussed before 1)-8). (7) (9) Selling (15) Buying (5) +Money(1) -Money(1) (14) (4) (6) (15) Selling & Buying (8) (14) -Stock (selling bonds) (12) (6) Bonds(3) (8) +Stock (buying bonds) (13) Bonds (only in buy bids)(10) Bonds (only in sell bids)(11) Fig.5. The NETFLOW scheme for exchange decision terminated with stock operations. The importance of each deal operation was estimated by the following procedure. Consequently ARCs CAPAC of the stock operations was assimilated to zero, and common variation of non-stock exchange volume in money terms was estimated. The more the difference of non-stock exchange money operation volume with and without the stock deal, the more important is considered stock exchange operation. 7/8

8 In our conditions the range of clients was of the order of 100, number of bonds was about 100, and number of bids was approximately Thus we described our way for optimization of non-stock exchanges between clients buying and selling different commodities. The integer-valued solution is founded using iterative netflow algorithm taking into account the whole net of commodities and cash flow, including the cash flows arising due to buy and sell sum mismatch. The system enables to store and to reproduce the initial conditions and final and intermediate results of obtained resolution in native SAS or external database. 8/8