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Beliefs and Settlement Risk

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Kimmo Soramaki
Kimmo Soramaki

The document discusses a model of settlement risk in a real-time gross settlement (RTGS) system. In the model: 1) Banks must decide whether to settle payments to counterparties or default, based on the value of settling versus defaulting given their beliefs about other banks' actions. 2) Banks update their beliefs over multiple rounds based on the history of actions, using a recency-weighted rule. 3) The model can converge to an equilibrium where all banks settle or a mixed equilibrium, depending on factors like the amount of money in the system, the distribution of money among banks, and the structure of the bank network.

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James McAndrews Federal Reserve Bank of New York Kimmo Soram辰ki Helsinki University of Technology www.soramaki.net For presentation at the Fifth Annual Bank of Finland Simulation Seminar 28 August 2007 The views expressed in these slides and presentation are the views of the authors and do not necessarily represent the views of the Federal Reserve Bank of New York or of the Federal Reserve System. Beliefs and Settlement Risk
In an RTGS system, participants face the problem of settlement risk . Failure of counterparty to settle as expected. Kahn, McAndrews, and Roberds (2003), and Mills and Nesmith (forthcoming) explore the issue. KMR examine a trading and settlement ring topology game. Settlement Risk
Model components: Ring topology game Time line 0 1 2 Trade, deliver Get money from respondents, Realize production, Produce Make payments Assets Money (M) Deliveries (F) from predecessors that settle Payments (P) from successors that settle 2 3 4 deliveries, production, payments, P ... ... 5 1 Predecessors deliver intermediate goods Consumption, F*(amount delivered) successors pay for good in period 2
If agents deliver and settle, all is well, because F>P, there is a positive gain from trade, and value from settling If default occurs, then parties must go to bankruptcy court. Debtor gets to keep 留 > 0 share of assets, Creditor gets 硫 >0 share. 留 + 硫 <1. Defaulter cant go to bankruptcy court as creditor. Settlement game
KMR show that for an open set of parameter values, there can be regions of mutually assured default and regions of mutually assured settlement , and these regions can overlap. High levels of money, M, assist in assuring settlement, as does collateral (shrink, or even eliminate region of mutually assured default). Here we interpret M to represent the behavior of a banks respondent network. Ring topology game
KMR assume agents adopt Nash equilibrium beliefs in a static environment. Here we adopt a dynamic fictitious-play-like procedure for agents to form beliefs that are consistent with the equilibrium actions of the agents. Update beliefs based on observed actions Recency weighting Play until beliefs and actions are stable Beliefs about Settlement Risk
Model components Assets Money (M) Deliveries (F) from predecessors that settle Payments (P) from successors that settle (F>P, denoting positive value from settling) Beliefs p i + , probability that successor pays p i - , probability that predecessor delivers 2 3 4 deliveries, F payments, P ... ... 5 1 predecessors 1 and 2 successors 3 and 4
Banks settle if value of settlement > value of defaulting Value of settlement + own assets - payments to all predecessors + creditors share ( 硫 ) of defaulting successors assets Value of defaulting + defaulters share ( ) of own assets Assets are contingent on other banks behavior. In order to decide whether to settle or default, banks must form beliefs about other banks behavior, and the behavior of their counterparts. Decision making
Value of settlement (S i ) Value of defaulting (D i ) Decision making (contd) assets by successor expected number of creditors by the successor
Banks update beliefs on the basis of experience. Recency-weighted update rule: Forming beliefs , 0=default, 1=settle 留 = weight parameter (we use 0.1)
Convergence example rounds banks white = settle, orange = default no convergence banks rounds convergence all settle equilibrium 0 0 100 100 0 ~300 ~300
identical M i identical initial beliefs and ring topology reach = number of outgoing/incoming links reach = 1 Money vs. network reach reach = 2 reach = 5
with given initial beliefs (here 0.2) and ring of reach 1 we investigate alternative mean preserving spreads of M i settlement equilibrium is possible with less money when money is distributed more unevenly Degree of heterogeneity mixed refers to a cycle or to a partial settle/default equilibrium
heterogeneous M i (uniform, carrier = 1 ) identical initial beliefs and ring topology reach = number of outgoing/incoming links Heterogeneity and reach reach = 2 reach = 5 reach = 1
Conclusions Our investigation of settlement risk has yielded three findings: increased money holdings, as in KMR, increase the likelihood of settlement heterogeneity of money holdings tends to improve outcomespositive contagion (antibodies rather than viruses) Initial beliefs matter in the selection of settle or default equilibrium, when both equilibria exist.

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Beliefs and Settlement Risk

  • 1. James McAndrews Federal Reserve Bank of New York Kimmo Soram辰ki Helsinki University of Technology www.soramaki.net For presentation at the Fifth Annual Bank of Finland Simulation Seminar 28 August 2007 The views expressed in these slides and presentation are the views of the authors and do not necessarily represent the views of the Federal Reserve Bank of New York or of the Federal Reserve System. Beliefs and Settlement Risk
  • 2. In an RTGS system, participants face the problem of settlement risk . Failure of counterparty to settle as expected. Kahn, McAndrews, and Roberds (2003), and Mills and Nesmith (forthcoming) explore the issue. KMR examine a trading and settlement ring topology game. Settlement Risk
  • 3. Model components: Ring topology game Time line 0 1 2 Trade, deliver Get money from respondents, Realize production, Produce Make payments Assets Money (M) Deliveries (F) from predecessors that settle Payments (P) from successors that settle 2 3 4 deliveries, production, payments, P ... ... 5 1 Predecessors deliver intermediate goods Consumption, F*(amount delivered) successors pay for good in period 2
  • 4. If agents deliver and settle, all is well, because F>P, there is a positive gain from trade, and value from settling If default occurs, then parties must go to bankruptcy court. Debtor gets to keep 留 > 0 share of assets, Creditor gets 硫 >0 share. 留 + 硫 <1. Defaulter cant go to bankruptcy court as creditor. Settlement game
  • 5. KMR show that for an open set of parameter values, there can be regions of mutually assured default and regions of mutually assured settlement , and these regions can overlap. High levels of money, M, assist in assuring settlement, as does collateral (shrink, or even eliminate region of mutually assured default). Here we interpret M to represent the behavior of a banks respondent network. Ring topology game
  • 6. KMR assume agents adopt Nash equilibrium beliefs in a static environment. Here we adopt a dynamic fictitious-play-like procedure for agents to form beliefs that are consistent with the equilibrium actions of the agents. Update beliefs based on observed actions Recency weighting Play until beliefs and actions are stable Beliefs about Settlement Risk
  • 7. Model components Assets Money (M) Deliveries (F) from predecessors that settle Payments (P) from successors that settle (F>P, denoting positive value from settling) Beliefs p i + , probability that successor pays p i - , probability that predecessor delivers 2 3 4 deliveries, F payments, P ... ... 5 1 predecessors 1 and 2 successors 3 and 4
  • 8. Banks settle if value of settlement > value of defaulting Value of settlement + own assets - payments to all predecessors + creditors share ( 硫 ) of defaulting successors assets Value of defaulting + defaulters share ( ) of own assets Assets are contingent on other banks behavior. In order to decide whether to settle or default, banks must form beliefs about other banks behavior, and the behavior of their counterparts. Decision making
  • 9. Value of settlement (S i ) Value of defaulting (D i ) Decision making (contd) assets by successor expected number of creditors by the successor
  • 10. Banks update beliefs on the basis of experience. Recency-weighted update rule: Forming beliefs , 0=default, 1=settle 留 = weight parameter (we use 0.1)
  • 11. Convergence example rounds banks white = settle, orange = default no convergence banks rounds convergence all settle equilibrium 0 0 100 100 0 ~300 ~300
  • 12. identical M i identical initial beliefs and ring topology reach = number of outgoing/incoming links reach = 1 Money vs. network reach reach = 2 reach = 5
  • 13. with given initial beliefs (here 0.2) and ring of reach 1 we investigate alternative mean preserving spreads of M i settlement equilibrium is possible with less money when money is distributed more unevenly Degree of heterogeneity mixed refers to a cycle or to a partial settle/default equilibrium
  • 14. heterogeneous M i (uniform, carrier = 1 ) identical initial beliefs and ring topology reach = number of outgoing/incoming links Heterogeneity and reach reach = 2 reach = 5 reach = 1
  • 15. Conclusions Our investigation of settlement risk has yielded three findings: increased money holdings, as in KMR, increase the likelihood of settlement heterogeneity of money holdings tends to improve outcomespositive contagion (antibodies rather than viruses) Initial beliefs matter in the selection of settle or default equilibrium, when both equilibria exist.