An agent-based model of payment systems<br />Marco GalbiatiKimmo SoramäkiNorges Bank, Oslo 24 March 2011<br />
Interbank Payment Systems<br />Source: Bech, Preisig, Soramäki (2008), FRBNY Economic Policy Review / September 2008<br />
The values are large<br /> ~1939 tr<br /> ~194 tr<br /> ~120 tr<br /> ~5 tr<br />
The liquidity is costly<br />Luckily central banks provide free intraday credit against collateral<br />But collateral has...
… payment arrival uncertain<br />Payment<br />System<br />Instructions<br />Payments<br />Liquidity<br />Summed over the n...
… liquidity dynamics are complex<br />Payment<br />System<br />Instructions<br />Payments<br />Liquidity<br />Reducing liq...
… and playing a game<br />In the collateralized credit game, early settlement (morning, morning) is a unique equilibrium i...
Objective and approach<br />To study liquidity demand in a payment system <br />The paper draws on:<br />Game theoretic mo...
Model<br />Consists of a sequence of days<br />At the beginning of each day<br />Identical banks simultaneously choose fun...
Aggregationproperty<br />Turns out, we can simplify the problem<br />In the long run (within a day), the distribution of l...
Whyis this?<br />The system can be understood as a Markov process<br />Transition probabilities for moving liquidity from ...
Convexity property of delays<br />Delays are a convex function of own and others’ liquidity<br />A upward shift of the cur...
… same “empirically”<br />Delays as a function of own and others’ liquidity (N=13)<br />
Costs<br />Recall, costs depend on own liquidity and others liquidity -> which jointly determine delays<br />Red = high pr...
Model parameters<br />2-30 banks, 400-6000 payments<br />Base case (15/3000) “looks like” CHAPS<br />Enough payments for p...
Liquidity demand<br />With “CHAPS” inferred liquidity price<br />-> Banks provide 3-10% less than planner<br />-> The cost...
More banks of same size<br />In a larger system liquidity gets lost…<br />Variance in cascade length (and bank’s incoming ...
… increase liquidity consumption<br />
… and increase costs<br />
Concentration increases efficiency<br />Same volume distributed across different number of banks<br />“Pooling effect”, ec...
… and reduces costs<br />
Summing up<br />The paper put together “realistic” liquidity dynamics with bank behavior<br />Derived liquidity demand fun...
Liquidity saving mechanisms<br />Galbiati and Soramäki (2010), BoE Working Paper No. 400<br />Extends the model with <br /...
Withholding vs two stream LSM<br />Withholding low priority payments<br />Submitting low priority payments to LSM stream<b...
Dynamics<br />Other banks use mostly LSM<br />Other banks use mostly RTGS<br />Other banks post little liquidity<br />Othe...
Equilibria<br />Low price of liquidity -><br />liquidity<br />threshold<br />-> High price of liquidity<br />
Mainresults<br />Planner virtually never uses LSM stream<br />Banks mix RTGS with LSM for a wide liq. price range<br />Ban...
Thank you!<br />More information at<br />www.financialnetworkanalysis.com<br />
An agent based model of payment systems - Talk at Norges Bank 24 March 2011
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An agent based model of payment systems - Talk at Norges Bank 24 March 2011

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The paper builds an agent based model where banks choose the amount of liquidity to settle a given flow of payments. The paper pays special attention to a realistic settlement process with complex dynamics and studies the equilibrium level of liquidity that is a result of the game between the banks. The paper investigates liquidity usage with various system sizes and volumes, and under different liquidity cost parameters.

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An agent based model of payment systems - Talk at Norges Bank 24 March 2011

  1. 1. An agent-based model of payment systems<br />Marco GalbiatiKimmo SoramäkiNorges Bank, Oslo 24 March 2011<br />
  2. 2. Interbank Payment Systems<br />Source: Bech, Preisig, Soramäki (2008), FRBNY Economic Policy Review / September 2008<br />
  3. 3. The values are large<br /> ~1939 tr<br /> ~194 tr<br /> ~120 tr<br /> ~5 tr<br />
  4. 4. The liquidity is costly<br />Luckily central banks provide free intraday credit against collateral<br />But collateral has a cost (explicit or opportunity)<br />The cost is perhaps around 8-16bp (research on eMid data, banks internal pricing)<br />Higher during crisis: Baglioniand Monticini (2010) say it was 10 times as high in 2007<br />And liquidity can be recycled during the day<br />Provide a free source of liquidity, amount to 90% of liquidity usage <br />Timing is uncertain, depends on other banks<br />Banks manage intraday liquidity<br />Synchronize payments with incoming liquidity -> to save on external liquidity<br />Delaying payments is also costly: sanctions, service levels, agreements, processing schedules <br />But it’s a hard problem…<br />
  5. 5. … payment arrival uncertain<br />Payment<br />System<br />Instructions<br />Payments<br />Liquidity<br />Summed over the network, instructions arrive at a steady rate<br />When liquidity is high payments are submitted promptly and banks process payments independently of each other<br />Source: Beyeler, Glass, Bech and Soramäki (2007), Physica A, 384-2, pp 693-718. <br />
  6. 6. … liquidity dynamics are complex<br />Payment<br />System<br />Instructions<br />Payments<br />Liquidity<br />Reducing liquidity leads to episodes of congestion when queues build, and cascades of settlement activity when incoming payments allow banks to work off queues. Payment processing becomes coupled across the network<br />1<br />1<br />
  7. 7. … and playing a game<br />In the collateralized credit game, early settlement (morning, morning) is a unique equilibrium if the opportunity cost of collateral is less than the cost of delaying(C < D). This outcome is efficient. <br />Conversely, late settlement (afternoon, afternoon) is a unique equilibrium if C > D, and the game is a prisoner’s dilemma. Late settlement is inefficient.<br />Source: Bech and Garratt (2006), Journal of Economic Theory and Bech (2008), FRBNY Economic Policy Review<br />
  8. 8. Objective and approach<br />To study liquidity demand in a payment system <br />The paper draws on:<br />Game theoretic models that incorporate behaviour: Angelini (1998), Chakravorti (2000), Bech and Garratt (2006)<br />Payment system simulations that bring more realism to complex dynamics and interactions in the settlement process: Koponen and Soramäki (1998), Leinonen, ed. (2005, 2007), Devriese and Mitchell (2005)<br />Agent based models for interaction between banks in a continuous game: Tesfatsion (2001), Axelrod and Tesfatsion(2006), Herbert (2007)<br />
  9. 9. Model<br />Consists of a sequence of days<br />At the beginning of each day<br />Identical banks simultaneously choose funds to commit that maximize expected payoff<br />Payoff depends on own and others’ choices <br />Consists of liquidity and delay cost component:<br />During<br />Payment simulation model (RTGS),<br />Poisson arrival of unit size payments, complete network<br />Banks follow simple rule: settle payment if liquidity, queue if not<br />At end<br />Banks receive payoff<br />Banks update beliefs on others’ choices<br />Banks update payoff for own/others liquidity combinations<br />After enough days banks converge to stable choices and beliefs<br />
  10. 10. Aggregationproperty<br />Turns out, we can simplify the problem<br />In the long run (within a day), the distribution of liquidity does not matter, only its total level does<br />For the short run, bank’sown liquidity mattersmore than total level<br />Banks maintain beliefs ontotal liquidity, and a payoffmatrix on own liquidity and total liquidity<br />Equal distribution<br />Highly skewed<br />
  11. 11. Whyis this?<br />The system can be understood as a Markov process<br />Transition probabilities for moving liquidity from i to j<br />Converges to a steady state (assuming no liquidity constraint)<br />Holds better <br />When convergence is fast (symmetric and complete network fastest)<br />The ratio of payments to liquidity is high<br />
  12. 12. Convexity property of delays<br />Delays are a convex function of own and others’ liquidity<br />A upward shift of the curve (more liquidity) reduces less delays (red area) the higher the curve is<br />balance<br />time<br />
  13. 13. … same “empirically”<br />Delays as a function of own and others’ liquidity (N=13)<br />
  14. 14. Costs<br />Recall, costs depend on own liquidity and others liquidity -> which jointly determine delays<br />Red = high price for liquidity, Blue = low price for liquidity<br />
  15. 15. Model parameters<br />2-30 banks, 400-6000 payments<br />Base case (15/3000) “looks like” CHAPS<br />Enough payments for property 1 to hold<br />Combinations explore different aspects of system size <br />Liquidity choices (for each bank)<br />From 0 (nothing settles) <br />To 50 (virtually no delays)<br />Price of liquidity<br />From free <br />Until equilibrium liquidity is 0<br />Price of delays is normalized to 1<br />
  16. 16. Liquidity demand<br />With “CHAPS” inferred liquidity price<br />-> Banks provide 3-10% less than planner<br />-> The cost might be ~35-75bp<br />
  17. 17. More banks of same size<br />In a larger system liquidity gets lost…<br />Variance in cascade length (and bank’s incoming payments) is increased<br />Due to convexity, increasing variance increases expected value<br />Delay per payment<br />
  18. 18. … increase liquidity consumption<br />
  19. 19. … and increase costs<br />
  20. 20. Concentration increases efficiency<br />Same volume distributed across different number of banks<br />“Pooling effect”, economies of scale<br />Argument for tiered structures<br />
  21. 21. … and reduces costs<br />
  22. 22. Summing up<br />The paper put together “realistic” liquidity dynamics with bank behavior<br />Derived liquidity demand function<br />Banks underprovide liquidity<br />Explored system size<br />Concentrating payments among a few banks is more efficient -> Tiering<br />Economies of scale in “pooling effect” but not in “open access” sense<br />
  23. 23. Liquidity saving mechanisms<br />Galbiati and Soramäki (2010), BoE Working Paper No. 400<br />Extends the model with <br />Payment urgency: [0,1]<br />Two streams of settlement: <br />RTGS – as in Galbiati and Soramäki (2008)<br />LSM – a partial netting algorithm as in Bech and Soramäki (2002)<br />An additional choice variable: urgency theshold above which payment is submitted to RTGS<br />Instead of “Fictitious play” uses a pre-calculated pay-off matrix and standard methods to solve it<br />Focus on symmetric equilibria<br />
  24. 24. Withholding vs two stream LSM<br />Withholding low priority payments<br />Submitting low priority payments to LSM stream<br />Priority threshold<br />
  25. 25. Dynamics<br />Other banks use mostly LSM<br />Other banks use mostly RTGS<br />Other banks post little liquidity<br />Other banks post much liquidity<br />
  26. 26. Equilibria<br />Low price of liquidity -><br />liquidity<br />threshold<br />-> High price of liquidity<br />
  27. 27. Mainresults<br />Planner virtually never uses LSM stream<br />Banks mix RTGS with LSM for a wide liq. price range<br />Banks generally underprovide liquidity<br />Banks are better off with LSM than without (less far from planner’s choice)<br />Bad equilibria are possible -> co-ordination may be needed when introducing them<br />
  28. 28. Thank you!<br />More information at<br />www.financialnetworkanalysis.com<br />

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