New approaches for payment system simulation research

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New approaches for payment system simulation
research

• Kimmo Soramäki
• ECB / HuT / BoE / FRBNY
• TKK, Helsinki, 3.9.2007

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Payment systems

• All economic and financial activity necessitates
  payments
• Payments need to be settled somehow
• Payments can be intra-bank or interbank
• For the latter need for a payment system
• Interbank payments account to 3 trillion a day
  in US 80 times the GDP on annual level
• Efficient and safe interbank payment systems are
  important for
• Efficient financial markets
• Financial stability
• Monetary policy
• Settling payments requires liquidity, which is
  costly
• In US liquidity worth 3 of daily flows are used
  for settlement, i.e. daily speed of circulation
  is 33.

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Papers

• Soramäki, Kimmo, M.L. Bech, J. Arnold, R.J. Glass
  and W.E. Beyeler (2007). "The Topology of
  Interbank Payment Flows". Physica A. Vol. 379.
• Models payment flows among banks as graphs
  (topology)
• Beyeler, Walter, M.L Bech, R.J. Glass, and K.
  Soramäki (2007). "Congestion and Cascades in
  Payment Systems". Physica A. Forthcoming.
• Models the coupling of payment flows and flow
  dynamics (physics)
• Galbiati, Marco and Kimmo Soramäki (2007).
  Dynamic model of funding in interbank payment
  systems . Bank of England Working Paper.
  Forthcoming.
• Models bank decision-making (behavior)

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Topology

• Payment system is modeled as a graph of
  liquidity flows (links) between banks (nodes)

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Fedwire liquidity flows
66 banks comprise 75 of value25 banks
completely connected
6600 banks, 70,000 links
Fedwire liquidity flows share many of the
characteristics commonly found in other empirical
complex networks - scale-free (power law)
degree distribution - high clustering
coefficient - small world phenomenon - short
paths (avg 2.6) in spite of low connectivity
(0.3) - structure of networks persistent from
day to day - heavily impacted by the terrorist
attacks of 9/11, disruption lasted for 10 days
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Physics

• Model of the dynamics that take place in
  payment system under simple rules of settlement
• Interaction of simple local rules gt emergent
  system level behaviour

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Influence of liquidity 1
Payment System
Instructions
Payments
Liquidity
Summed over the network, instructions arrive at a
steady rate
When liquidity is high payments are submitted
promptly and banks process payments independently
of each other
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Influence of liquidity 2
Payment System
Instructions
Payments
Liquidity
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
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Influence of liquidity 3
Payment System
Instructions
Payments
Liquidity
At very low liquidity payments are controlled by
internal dynamics. Settlement cascades are
larger and can pass through the same bank
numerous times
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Influence of a liquidity market
Payment System
Instructions
Payments
Liquidity Market
A liquidity market substantially reduces
congestion using only a small fraction (e.g. 2)
of payment-driven flow
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Behavior

• Modeling banks as decision makers where each
  banks best action depends on the actions of
  other banks.

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Funding behavior model

• Banks choose an opening balance at the beginning
  of each day
• Banks face uncertainty about the opening balances
  of other banks
• Banks face funding costs and delay costs, which
  depend on the opening balances (and the random
  arrival of payment instructions).
• Banks adapt their level of opening balances over
  time (by means of Fictitious play), depending on
  observed actions by others
• The game is played until convergence of beliefs
  takes place

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Illustration of costs and best replies

• Costs are minimized at different liquidity
  levels, depending on liquidity posted by other
  banks, e.g. (for n15, delay cost5)
• if others post 1, I should post 24
• if others post 5, I should post 15
• if others post 50, I should post 10

funds committed by ltjgt
cost, i
funds committed by i
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Results 1 base case
for n15 200 payments of unit size per bank

• Banks (naturally) use more liquidity when delay
  price is high
• The amount used increases rapidly as delay price
  is increased from 0
• Banks will practically not commit over 49 units

funds committed by i
funds committed by i
price of delays
price of delays
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Conclusions

• Performance of a payment system is a function of
  topology, physics and behavior one factor alone
  is not enough to evaluate efficiency or
  robustness
• Graph theory provides good tools for analyzing
  the structure of interbank payment systems and
  their liquidity flows and e.g. for identifying
  important banks
• Statistical mechanics help understand the impact
  of settlement rules on system performance (simple
  local rules -gt emergent system level behavior)
• Depending on topology, physics and cost
  parameters, different liquidity games emerge,
  and thus different system level behavior
• The complete model developed in conjunction with
  the presented work is modular (programmed in
  Java) and can be easily enriched and used to
  analyze real policy questions (not only interbank
  payments)

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Topology and disruption 1
example Fedwire around 9/11 2001