real-time gross settlement and hybrid payment systems: a comparison
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Real-Time Gross Settlement and Hybrid Payment Systems: A
ComparisonMatthew WillisonBank of England
The views expressed in this paper are those of the author, and do not necessarily reflect those of the Bank of England.
Background
• DNS versus RTGS
credit risk versus liquidity demands.
• Hybrids
no credit and settlement risk but more liquidity efficient (?).
Literature Review
• BIS Report (1997)
• McAndrews and Trundle (2001)
• Roberds (1999)
• Simulations; e.g., Johnston et al. (2003)
Aim of the paper
• Assess the welfare properties of RTGS and hybrid payment systems.
• But while allowing bank behaviour to fully depend on the payment system design in place.
Criteria
• Liquidity demands (≡ Collateral posted)
• Speed of settlement ( system’s exposure to operational risk)
• First-best: - Total collateral posted is
minimised.
- All payments are settled early
in the day.
The Model
• n (settlement) banks; n>2
• All payments have a value = 1
• Each bank has a single payment to send
to each other bank
• A payment between bank i and bank j;
i→j
The Model
• Two periods: morning and afternoon
• Collateral costs:
- ¹ per unit in the morning
- ² per unit in the afternoon
The Model
¹ ² a bank only posts collateral in
the morning that it uses in the morning.
• Morning payments can be used to make
afternoon payments.
• Afternoon payments can be used to repay
the CB at the end of the day.
The Model
• Delay cost; incurred when a payment is
not settled in the morning.
• Delay cost, (i→j)
(i→j) takes one of n-1 possible values.
The Model
(i→j)=(i→k) iff j=k
• Highest (i→j)>¹
• Lowest (i→j) ¹- ²
The Model
• Delay costs are bank’s private information;
I.e., only i knows (i→j)
• A bank forms internal queue Qi
• Position of payment in Qi is inversely related to its delay cost.
The Model
• Cancellation cost,
• Incurred when a payment is not settled in the afternoon, given that it is not settled in the morning.
> ²
RTGS
Banks borrow liquidity from the CB
Banks makepayments
Banks borrow liquidity from the CB
Banks makepayments
Banks repaythe CB
Morning Afternoon
RTGS
• Morning action:
• Morning action set:
• Afternoon action:
• Afternoon action set:
}},1{\},...,2,1{},1{{ ii QnQ
1ia
2ia
)\( 1ii aQ
Afternoon
> ²; optimal for a bank to settle all remaining payments in the afternoon, for any
• Value of i’s afternoon payments is
},...,{ 111 naa
1)1( ian
Morning
• A bank is affected by other banks’ morning
actions through effect on afternoon
collateral needs.
• Internal queue ordering is private
information a bank is uncertain about
the value of its incoming payments in the
morning.
Morning
• Bank chooses morning action to minimise
expected total cost.
• Expected total cost = Morning collateral
cost + Delay cost + Expected afternoon
cost
Morning collateral cost
Delay cost
Morning collateral cost + Delay cost
Total cost
Cost
Value of morning payments
0 1 n-1
Equilibrium
• Equilibrium (in pure strategies)
*)(* 11iii aBRa
i*\* 12iii aQa
Equilibrium
• Each bank settles at least one payment in the morning because (1)>¹
• {Q1,…,Qn} is not an eqm. because expected afternoon collateral costs = 0 and (n-1)<¹
Hybrids
• Two ways of settling a payment: RTGS and offset.
• Offset: a payment has to be submitted to the central queue.
Hybrids
• H1: Offset in the afternoon
• H2: Offset in the morning
• H3: Offset in both periods
Hybrids
• Central queue transparency: - Opaque; a bank cannot see other banks’ payments in the central queue. - Visible; a bank can see payments to it in the central queue.
• May effect how well banks co-ordinate use of the central queue.
Hybrids
• Split each period into two sub-periods.
• Sub-periods, 1a, 1b, 2a, 2b.
• Results for RTGS with four sub-periods are the same as those with two periods.
Hybrids
• Placing a payment in the central queue in one sub-period is not ≡ a commitment to keep the payment in the central queue in subsequent sub-periods.
• Submission behaviour depends on what a bank expects other banks to do.
Hybrids
there is the potential for co-ordination problems.
• Not guaranteed that visibility will overcome problems.
H1
• If j→i is received in the morning, i→j is settled by RTGS in the afternoon.
• All RTGS payments settled in 2b.
H1
• If j→i is not received in the morning, a bank submits i→j to the central queue in 2a if each other bank submits at least one payment.
• Because each payment should be offset with a positive probability.
H1
• So all payments that can be offset will be
offset in 2a.
• If a payment is offset, needs no liquidity.
H1
• If a payment is settled by RTGS in 2b, the
offsetting payment arrived in the morning.
So need no liquidity.
• Expected afternoon collateral = 0
Morning collateral cost
Delay cost
Morning collateral cost + Delay cost
Total cost
Cost
Value of morning payments
0 1 n-1RTGS
H1
H1
• Bank’s cost minimisation problems are disentangled from each other.
• Each bank settles the same value of payments in the morning (have the same cost structure).
H1
• Value of morning payment in H1 value of morning payments under RTGS.
• Liquidity in H1 liquidity in RTGS
• H1 is not necessarily better than RTGS.
H2
• In 2a, a bank submits all payments if each other bank submits at least one payment.
• Because each payment could be settled with positive probability.
• All payments offset in 1a.
H3
• In 2a, a bank submits all payments if each other bank submits at least one payment.
• Because each payment could be settled with positive probability.
• All payments offset in 1a.
H2 and H3
• First-best since all payments are offset ( no liquidity required) in sub-period 1a.
Delay costs are private information
• Under H2 and H3 there exist ‘bad’ equilibria where the central queue is not used at all in 1a.
• But no intermediate cases because each payment could be settled with positive probability if each other bank submits 1 payment.
Delay costs are private information
• If delay costs are public information we
can show there exist intermediate cases,
where some but not all payments are
submitted to the central queue in 2a.
Conclusion
• The first-best is attained under Hybrid payment systems if offset is available in the morning.
• Offering offset in the afternoon can only be as good than RTGS.
Conclusion
• Central queue transparency is unimportant.
• Maybe because of the information structure and that the cost of using the central queue = 0
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