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