Presentazione di PowerPoint

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An agent-based model of payment systems
Marco Galbiati Bank of England Kimmo
Soramäki Helsinki Univ. of Technology / ECB
ECB-BoE Conference Payments and Monetary and
Financial Stability 12-13 November 2007
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Overview of the presentation
Motivation, related work
Model
Results
Conclusions
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Overview of the presentation
Motivation, related work
Model
Results
Conclusions
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Overview of the presentation
Motivation, related work
Model
Results
Conclusions
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Overview of the presentation
Motivation, related work
Model
Results
Conclusions
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Overview of the presentation
Motivation, related work
Model
Results
Conclusions
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Liquidity in payment systems
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Liquidity in payment systems
Deferred Net Settlement vs Real Time Gross
Settlement
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Liquidity in payment systems
Deferred Net Settlement vs Real Time Gross
Settlement
Liquidity risk (and operational risk)
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Liquidity in payment systems
Deferred Net Settlement vs Real Time Gross
Settlement
Liquidity risk (and operational risk)
Liquidity as a common good
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Liquidity in payment systems
Deferred Net Settlement vs Real Time Gross
Settlement
Liquidity risk (and operational risk)
Liquidity as a common good
Liquidity is costly tradeoff cost-of-liquidity /
cost-of-delay
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Related literature
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Related literature
Simulations Koponen-Soramaki (1998), Leinonen,
ed. (2005, 2007) Work at BoE, BoFr, US Fed, BoC,
BoFin, others. Use actual payment data and
investigate alternative scenarios effect on
payment delays, liquidity needs, and risks
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Related literature
Simulations Koponen-Soramaki (1998), Leinonen,
ed. (2005, 2007) Work at BoE, BoFr, US Fed, BoC,
BoFin, others. Use actual payment data and
investigate alternative scenarios effect on
payment delays, liquidity needs, and risks
Game theoretic models Angelini (1998),
Bech-Garrat (2003), McAndrews (2007) Investigate
"liquidity management games" to analyze intraday
liquidity management behavior of banks in a RTGS
(and DNS) environment
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Model overview
RTGS á la UK CHAPS banks choose an opening
balance at the beginning of each day, used to
settle payments during the day. Banks face a
random stream of payment orders, to be settled
out of their liquidity. Beside funding costs,
banks (may) experience delay costs
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Model overview
RTGS á la UK CHAPS banks choose an opening
balance at the beginning of each day, used to
settle payments during the day. Banks face a
random stream of payment orders, to be settled
out of their liquidity. Beside funding costs,
banks (may) experience delay costs
Banks adapt their opening balances over time,
learning from experience, until equilibrium is
reached We look at properties of equilibrium
liquidity
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Model overview
RTGS á la UK CHAPS banks choose an opening
balance at the beginning of each day, used to
settle payments during the day. Banks face a
random stream of payment orders, to be settled
out of their liquidity. Beside funding costs,
banks (may) experience delay costs
Banks adapt their opening balances over time,
learning from experience, until equilibrium is
reached We look at properties of equilibrium
liquidity
We consider two scenarios normal conditions
and operational failures
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Settlement algorithm
i receives order to pay to j
time
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Settlement algorithm
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
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Settlement algorithm
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
if j has queued payments, the first one (say to
k) is settled
else, the order is queued
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Settlement algorithm
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
if j has queued payments, the first one (say to
k) is settled
if k has queued payments, the first one (to ...)
is settled
else, the order is queued
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Settlement algorithm
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
if j has queued payments, the first one (say to
k) is settled
if k has queued payments, the first one (to ...)
is settled
... cascade ends when the recipient of the
payment has no queued payments
else, the order is queued
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Settlement algorithm
k receives order to pay to z
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
if j has queued payments, the first one (say to
k) is settled
if k has queued payments, the first one (to ...)
is settled
the algorithm is run 30 million times, for
different liquidity levels
... cascade ends when the recipient of the
payment has no queued payments
else, the order is queued
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Settlement algorithm
k receives order to pay to z
i receives order to pay to j
time
if i has funds the order is settled j receives
funds
if j has queued payments, the first one (say to
k) is settled
if k has queued payments, the first one (to ...)
is settled
the algorithm is run 30 million times, for
different liquidity levels
... cascade ends when the recipient of the
payment has no queued payments
else, the order is queued
Payment orders arrive according to a Poisson
process. Each bank equally likely as sender/
recipient ? complete symmetric network
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Settlement algorithm

• Distribution of others liquidity does not matter
  (much), only total level does

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Settlement algorithm

• Distribution of others liquidity does not matter
  (much), only total level does

Delays
funds committed by i
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Settlement algorithm

• Distribution of others liquidity does not matter
  (much), only total level does

Delays
Costs
Costs
funds committed by i
funds committed by i
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The liquidity game

• Costs minimized at different liquidity levels,
  depending on others funds ? each bank plays a
  two-player game

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The liquidity game

• Costs minimized at different liquidity levels,
  depending on others funds ? each bank plays a
  two-player game

Best reply

• 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 others
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Learning the equilibrium
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Learning the equilibrium
Banks adapt actions over time, on the basis of
experience (Fictitious play) up to equilibrium.
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Learning the equilibrium
Banks adapt actions over time, on the basis of
experience (Fictitious play) up to equilibrium.
Property of Fictitious Play IF actions
converge to a pure profile (or to a
distribution) THEN that is a Nash equilibrium
of the game
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Learning the equilibrium
Banks adapt actions over time, on the basis of
experience (Fictitious play) up to equilibrium.
Property of Fictitious Play IF actions
converge to a pure profile (or to a
distribution) THEN that is a Nash equilibrium
of the game
In our case, actions do converge We show
(analytically) that given cost parameters, all
possible equilibria feature same average
liquidity So we can speak about the equilibrium
liquidity demand
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Total costs
price of delays 1
price of delays 2
funds committed by others
funds committed by others
funds committed by ltjgt
cost, i
cost, i
funds committed by i
funds committed by i
price of delays 5
price of delays 20
funds committed by others
funds committed by others
cost, i
cost, i
funds committed by i
funds committed by i
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Base case results
(15 banks)

• Banks (naturally) use more liquidity when delay
  price is high
• At price parity, banks commit exactly 1 unit
• The amount used increases by 13-15 units per
  bank (200-230 for the system) for each 10-fold
  increase in the price of delays
• Banks will practically not commit over 49 units

funds committed
delays
price of delays
funds committed by i
10-fold decrease for each 20 units of liquidity
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Efficiency

• The outcome is not efficient
• Higher levels of liquidity would yield overall
  lower costs

liquidity
costs
price of delays
price of delays
orange best non-equilibrium common action
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System size, fixed turnover by bank

• Banks post more liquidity for a given payment
  volume, the more other banks there are in the
  network
• Due to higher variation in the time to receive
  your own funds back

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System size, fixed total turnover

• Concentrated systems are more liquidity efficient
• Smaller number of banks -gt higher value of
  payments per bank -gt economies of scale

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Operational incident 1
increase in delays

• One bank can receive, but cannotsend for first
  half of the day (liquidity sink)
• Delays of non-incident banksare increased
• More so, when liquidity is scarce
• We expect banks to choose inequilibrium a higher
  level of liquidity
• e.g. (with delay cost 4)
• if others choose 14, in normal circumstances I
  should choose 10, in case of an incident 14

funds committed by ltjgt
increase in delays for i (0,1)
funds committed by i
example of changed behavior
cost, i
funds committed by i
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Operational incident 2

• With low delay cost, only small difference
• As delays get costlier, more liquidity is used
• At extremely high delay cost, adding funds does
  not help

funds committed by i
price of delays
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Conclusions

• We developed a model with endogenous decisions by
  banks on their level of funding
• We investigated the game with more realistic
  costs from settlement than analytical game
  theoretic models
• The game collapses to me vs. others as only the
  aggregate behavior of others is relevant. The
  type of the game depends on model parameters
  (system size and delay cost)
• Equilibrium
• not a social optimum
• more participants, fewer payments par bank and
  higher delay costs ? more liquidity
• Operational incident impact on liquidity holdings
  is ambiguous
• payoffs are not improved in equilibrium
• Model being extended to account for alternative
  delay cost specifications, and heterogeneous
  banks -gt policy purposes of Bank of England