Central counterparty (CCP) resolutionThe right move at the right time.

Umar Faruqui, Wenqian Huang and Takeshi ShirakamiBIS

15 November, 2018

Disclaimer: The views expressed here are those of the authors and notnecessarily of the Bank for International Settlements

Motivation

I CCPs are systemic nodesI Increasing proportion of central clearing

Data source: BIS

I CCP resilience, recovery and resolution are essential tofinancial stability

I Entering into CCP resolution is an irreversible decision underuncertainty

I Timing is important

Key trade-off and preliminary findings

This paper develops a real option model

I Optimal stopping problem to minimize expected lossesI Too early

I Lose the option value of waiting

I Too LateI Losses could be extremely large and threaten financial stability

Preliminary findings

I Additional resources dedicated to CCP resolution

I The probability of CCP recovery is higherI Conditional on resolution, expected losses are larger

Literature review

I CCP recovery and resolution

I [Elliott(2013)],[Duffie(2014)]I [Raykov(2016)],[Singh and Turing(2018)]

I Central clearing

I [Duffie and Zhu(2011)],[Cont and Kokholm(2014)],[Kubitza, Pelizzon, and Getmansky(2018)]

I [Koeppl and Monnet(2013)], Biais, Heider and Hoerova (2012,2016, 2018)

I [Domanski, Gambacorta, and Picillo(2015)], [Cont(2017)]

I Real option

I [McDonald and Siegel(1986)],[Dixit(1989)]I [Pindyck(1990)], [Dixit and Pindyck(1994)]

Institutional background

Model setup - Agents

I Buyers

I expose to real economy riskI fully hedge with a (long-dated) derivatives contract

I Sellers

I make market for the derivativesI could default due to large price movements

I A CCP

I sits between the buyers and the sellersI has one recovery tool following its rule book

I A resolution authority

I minimizes expected losses from CCP recoveryI decides when to resolve the CCP

Model setup - Default scenario

VM receivable

LIBOR(Defaulting)

Fix(Defaulting)

VM payable

Liquid assets

t=-1

- LIBOR increases- Buyers and sellers need to exchange VM- Sellers default- The CCP needs to cover the default losses

IMDF

Equity

LIBORFix

Asset LiabilityCCP

Model setup - Recovery starts

VM receivable

LIBOR(Defaulting)

Fix(Defaulting)

VM payable

Liquid assets

t=-1

IMDF

Equity

LIBORFix

Asset LiabilityCCP

Liquid assets

Remaining losses

t=0 (trigger recovery)

VM payable

LIBORFix

Liquid assets IMEquity

Asset LiabilityCCP

LIBOR(Defaulted)

Fix(Defaulted)

- The prefunded resources are exhausted- The CCP needs to use recovery tools- Recovery tools

- Cash calls- VMGH

- Uncertainties- Market risk- Liquidity risk

Model setup - uncertainties

I Liquidity events

dNt =

0, 1− λtdt1, λtdt

I Cash inflow Rtdt

dRt = −εRtdNt

I Marked-to-market lossesXtdt

dXt = σtXtdzt

0.0 0.5 1.0 1.5 2.0Time

0.9800

0.9825

0.9850

0.9875

0.9900

0.9925

0.9950

0.9975

1.0000

R t (C

ash

inflo

ws)

0.0 0.5 1.0 1.5 2.0Time

0.90

0.95

1.00

1.05

1.10

X t (C

ash

outfl

ows)

Model setup - interlinked uncertainties

I When Xt

Rtis large, the CCP is less likely to recover

I Derivatives market get more volatile =⇒ σt is largeI Participants are less willing to provide liquidity =⇒ λt is large

Model setup - Successful recovery

VM receivable

LIBOR(Defaulting)

Fix(Defaulting)

VM payable

Liquid assets

t=-1

IMDF

Equity

LIBORFix

Asset LiabilityCCP

Liquid assets

Remaining losses

t=0 (trigger recovery)

VM payable

LIBORFix

Liquid assets IMEquity

Asset LiabilityCCP

LIBOR(Defaulted)

Fix(Defaulted)

Liquid assetsCash calls/VMGH

VM payable

LIBORFix

Liquid assets IMEquity

Asset

Liability

LIBOR(Defaulted)

Fix(Defaulted)

t=

- Cash calls are honored

- Cash outflows decrease

- CCP is recovered successfully

Model setup - CCP resolution

VM receivable

LIBOR(Defaulting)

Fix(Defaulting)

VM payable

Liquid assets

t=-1

IMDF

Equity

LIBORFix

Asset LiabilityCCP

Liquid assets

Remaining losses

t=0 (trigger recovery)

VM payable

LIBORFix

Liquid assets IMEquity

Asset LiabilityCCP

LIBOR(Defaulted)

Fix(Defaulted)

t=T

Liquid assetsCash calls/VMGH

VM payable

LIBORFix

Liquid assets IMEquity

Uncovered losses- Cash calls are not

honored- Cash outflows increase- The resolution

authority steps in

Asset LiabilityCCP

LIBOR(Defaulted)

Fix(Defaulted)

Optimal stopping problem

The resolution authority solves the following stopping problem

maxT

E

∫ T

0

Inflow︷︸︸︷Rt −

Outflow︷︸︸︷Xt

dt

︸ ︷︷ ︸recovery

+

Equity︷︸︸︷e −

Inefficiency︷︸︸︷l +RT − XT

︸ ︷︷ ︸

resolution

:= F (R,X )

(1)

I Let ut denote the state variables: Rt ,XtI π(ut) = Rt − Xt and Ω(ut) = e − l + Rt − Xt

I Hamilton-Jacobi-Bellman (HJB) equation

F (ut) = maxπ(ut)dt + F (ut) + E [dF (ut)]︸ ︷︷ ︸recovery/continuation

, Ω(ut)︸ ︷︷ ︸resolution/stop

Optimal timing

I Optimal stopping regions are separated by threshold u∗

I Optimal timing of entry into resolution T

I The first time when ut reaches u∗

I Successful recovery timing τ (≥ 1)

I The first time when∫ τ

0

(Rt − Xt

)dt ≥ 0

I Resolve the CCP if T < τ

State variablesI It is optimal to resolve the CCP when Rt is small or Xt is largeI One can reduce the number of state variables to one: Gt = Xt

Rt

0.8

0.9

1.0

1.1

1.2Gt (Ratio between cash outflow and inflow)

G *

Successful recovery

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Time

0.15

0.10

0.05

0.00

0.05

0.10Rt Xt (Net cash inflow)

R * X *

Successful recovery

Additional resources dedicated to resolution

Proposition. Comparative staticsWith increasing additional resources dedicated to CCPresolution,(i) the expected time to resolution increases,(ii) the likelihood of successful recovery increases,(iii) the losses conditional on resolution increases.

Additional resources dedicated to resolutionWe establish a set of parameters for the base case

I ln(Xt) has a variance of 1% per period (σ = 0.1)

I Liquidity event comes once per period (λ = 1)

I 10% of the surviving members suffer losses (ε = 0.1)

I Resolving the CCP leads to 1 unit of asset (e − l = 1)

I Initial loss is 10 unit (R0 = X0 = 10)

I Additional resources of 1 unit (∆e = 1)

Limitations/Extensions

I The current model assumes auctions fail

I With successful auctions, the uncertainty on the cash outflowis resolved σt = 0

I The option value of waiting will be smallerI The same logic should carry through

I The model assumes away the buyers and sellers’ incentives

I Resolution by the authority may weaken the buyers and sellers’incentives to cooperate in the default management

I Taking into account the dynamic incentives of the buyers andsellers, the current thresholds might be too lenient.

I The base case calibration is rudimentary

I Liquidity/credit stress testing results from CFTC and ESMAI Any other suggestions?

Appendix

Uncertainties - VMGH

I Unlike cash calls, VMGH allows the CCP to directly reduce itsliability

Rtdt = Xtdt

I XtRt

= 1, i.e., the optimal stopping problem is not affected bythe interlinkage of the uncertainties

I CCP’s cash inflow Rt follows a geometric Brownian motion:

dRt = σRtdzt .

Optimal stopping problem - VMGH

The resolution authority solves the following stopping problem

maxT

E

[∫ T

0(−Ct) dt + (e − l − CT )

]:= V (C ) (2)

I Hamilton-Jacobi-Bellman (HJB) equation

V (Ct) = max

(−Ctdt + E [V (Ct) + dV (Ct)])︸ ︷︷ ︸Recovery

, (e − l − CT )︸ ︷︷ ︸Resolution

State variables - VMGH

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Time

0.05

0.04

0.03

0.02

0.01

0.00

Ct (Losses of the CMs)C *

Successful recovery

References I

Cont, Rama. 2017.“Central clearing and risk transformation.” .

Cont, Rama and Thomas Kokholm. 2014.“Central clearing of OTC derivatives: bilateral vs multilateralnetting.”Statistics & Risk Modeling 31 (1):3–22.

Dixit, Avinash. 1989.“Entry and exit decisions under uncertainty.”Journal of political Economy 97 (3):620–638.

Dixit, Avinash K and Robert S Pindyck. 1994.Investment under uncertainty.Princeton university press.

References II

Domanski, Dietrich, Leonardo Gambacorta, and CristinaPicillo. 2015.“Central clearing: trends and current issues.” .

Duffie, Darrell. 2014.“Resolution of failing central counterparties.”Available at SSRN 2558226 .

Duffie, Darrell and Haoxiang Zhu. 2011.“Does a central clearing counterparty reduce counterpartyrisk?”The Review of Asset Pricing Studies 1 (1):74–95.

Elliott, David. 2013.“Central counterparty loss-allocation rules.”Bank of England Financial Stability Paper (20):16.

References III

Koeppl, Thorsten V and Cyril Monnet. 2013.“Central counterparty clearing and systemic risk insurance inOTC derivatives markets.”Revue dconomie financire 109.

Kubitza, Christian, Loriana Pelizzon, and Mila Getmansky.2018.“The pitfalls of central clearing in the presence of systematicrisk.” .

McDonald, Robert and Daniel Siegel. 1986.“The value of waiting to invest.”The quarterly journal of economics 101 (4):707–727.

Pindyck, Robert S. 1990.“Irreversibility, uncertainty, and investment.”Tech. rep., National Bureau of Economic Research.

References IV

Raykov, Radoslav S. 2016.“To share or not to share? Uncovered losses in a derivativesclearinghouse.”Tech. rep., Bank of Canada Staff Working Paper.

Singh, Manmohan and Dermot Turing. 2018.“CCP Resolution - An Unresolved Problem.” .