endogenous derivatives networks. - banque de france fileendogenous derivatives networks. guillaume...

Endogenous Derivatives Networks.

Guillaume Vuillemey 1,2 Regis Breton 2

1Sciences-Po, Department of Economics

2Banque de France

ACPR - Banque de France - SoFIE, July 2014

Vuillemey and Breton (2014) Endogenous Derivatives Networks

Disclamer

Any opinions expressed are only the presenter's own and should not

be regarded as opinions of the Bank of France or the Eurosystem.


This paper

Question: How is the network for OTC derivatives likelyto change as a consequence of the OTC derivativesmarket reform?

Central clearing set to become mandatory (Dodd-Frank,EMIR).First channel: Increased demand for safe collateral assets tomeet increased margin requirements.Neglected channel: Changes in network size and structure.

The model

OTC derivatives network formation model.Both prices and quantities are negociated.Both idiosyncratic counterparty risk and (exogenous)collateralization and clearing requirements are accountedfor in banks' decision to trade.


Motivation

Same network of net CDS exposures.

No central clearing (left chart), full central clearing (rightchart).

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CCP clearing and collateral requirements

Wide range of estimates for required additional marginrequirements.

ISDA (2011): 1000 bn USD for IR swaps.IMF (2012): 100-200 bn USD for all OTC derivatives.Heller and Vause (2012): 720 bn USD for IR swaps and CDS.Due, Scheicher and Vuillemey (2014): Estimates for severalmarket structures.

Main limitation of previous studies: Neglect of the fact

that the network of exposure is endogenous to the

collateralization and clearing requirements.


CCP clearing and collateral requirements

Focus instead on changes in the market structure.

The net benet of opening a derivative exposure depends onthe relative weighting of costs and benets of collateral andclearing.Costs: Exposures that have the lower net expected marginalbenet may disappear if increased collateral requirements areimposed ceteris paribus.Benets: Or, alternatively, increased collateral requirementsmay induce some counterparties to trade more, as counterpartyrisk is then mitigated.

Results underpinned by bank trading behaviour

What if counterparty risk increases?What if the safe asset becomes scarcer?

Rough assessment of collateral demand mis-estimation when

network exogeneity is assumed.


Contribution

New model of OTC derivatives network formation.

Accounts for features of derivative networks (upfront payment,o-balance sheet exposure).Collateralization and clearing requirements enter banks'objective functions.Counterparty credit risk as a key ingredient.Both prices and quantities negociated.

Investigate the eect of three regulatory schemes.

Increased collateralization of bilateral exposures.Rehypothecation or not of collateral received.Increased scope for central clearing.


Preview of the results

Main results.

Market liquidity / intermediary activity decreases with highercollateral requirements.Some end-users are no longer able to obtain credit riskprotection.Rehypothecation does not change the ability of end-users toobtain credit risk protection, but increases market liquidity.Overall: Redistributive eects.

Additional results.

Increased counterparty risk reduces market size to a largeextent. Collateralization can mitigate the market shrinkage.A drop in the safe asset supply has a rst-order eect onmarket outcomes. Market changes due collateralizationrequirements are second-order in this context.


Related literature

Endogenous network formationNetwork models: Acemoglu et al. (2013), Battiston et al.(2012), Bluhm et al. (2013), Babus (2013).

Reviews by Dutta and Jackson (2003), Jackson and Zenou(2013).

OTC markets: Due et al. (2005, 2007).

Central clearing

Theoretical: Acharya and Bisin (2013), Biais et al. (2012,2013), Koeppl and Monnet (2010), Due and Zhu (2011).Empirical: Heller and Vause (2012), Sidanius and Zikes(2012), Singh (2013), Due et al. (2014).


Model - Notations

Set Ω = 1, ..., n of nancial institutions indexed by i .

Three dates t = 0, 1, 2.Stylized balance sheet of i ∈ Ω.

Riskless securities ci .

Gross yield r0 > 1 at t = 2 with probability one.

Risky credit exposures ai .

Gross yield R > r0 > 1 at t = 2 with probability (1− δ1).Gross yield 0 with probability δ1.δ1 observed only at t = 1.Imperfect signal δ0 = E [δ1] at t = 0.

The portfolio ai , ci is exogenously given at t = 0.

Vector of idiosyncratic bank probabilities of defaultΛ = λ1, ..., λn.

Provides a rationale for collateralizationAssumption: Independence of any λi and λj .The joint probability of i and j failing at t = 2 is λiλj .


Model - CDS contracts

Assumption: The risky asset a is illiquid and in xed supply.

Thus, instead of trading a for c, c is traded against creditderivatives written on a.

Consider CDS contracts on reference entity a.

OTC contract between i and j dened by the tuple ωij , pij.ωij ∈ R: Gross notional amount.

ωij > 0 in case i sells the contract.ωij = −ωji

pij > 0: Premium per unit of notional

pij (xed leg) paid at t = 0 by the buyer.

Proceeds invested in the safe asset, yielding ωjipij r0 at t = 2.

In case of default at t = 2 (w. p. δ1), the seller j pays −ωijR .


Model - Timing

Initial period: t = 0

Each bank i observes its portfolio ai , ci.δ0 ∈ [0; 1] is observed and the p.d.f. of δ1, denoted π (δ1)(with c.d.f. Π), is common knowledge.Banks are matched and credit derivatives are traded over alarge number of subperiods s = 1, ...,S.Initial margins are posted (with the riskless asset c).

Interim period: t = 1

True asset probability of default δ1 is observed.Change from δ0 to δ1 gives ground for variation marginsposting.

Final period: t = 2

All assets mature.In case a defaults, CDS payments take place.


Model - Trade without collateral

Banks mawimize VNM expected utility V = E [U].Utility of a bank when it fails normalized to U(0).Expected utility for i when being oered a contract ωij , pijwith j :

Vi (ωij , pij) =

∫ 1

0

π (δ1)[λiU (0) + (1− λi)

[(1− δ1)U (Ci + aiR)

+δ1[(1− λj)U (Ci − ωijR)

+λjU (Ci −max 0;ωijR)]]dδ1

With Ci ≡ (ci + ωijpij) r0.Both asset default probability and counterparty defaultprobability are accounted for.


Model - Trade without collateral

Both ωij and pij are negociated.

Any bank i can thus be both buyer and seller.

Objective: Nash product with equal bargaining power:

ωij , pij ∈ arg max (Vi (ωij , p)− Vi (0, .)) (Vj (ωji , p)− Vj (0, .))

Subject to budget and incentive-compatibility constraints :−pijωij ≤ ci(cj + pijωji ) r0 ≥ ωjiR

Vi (ωij , pij)− Vi (0, .) ≥ 0

Vj (ωji , pij)− Vj (0, .) ≥ 0

Note: Naked CDS buying is allowed.


Model - Matching

Period t = 0 is divided into a large number S of sub-periods

indexed by s.

At each s, a randomly chosen pair of banks is matched.

Preferential attachment is modeled and parameterized.

Fixed cost κ of creating a rst link with a counterparty.

Limited rationality: A bank considers each match as the last

trading opportunity before S .


Model - Collateral requirements

Rationale for collateralization: idiosyncratic probabilities of

default Λ.

Collateralization requirements are exogenously given.Initial margins

Meant to cover potential future exposure.

χIMji = τ IM f IM · σ (δ1)max 0;ωji

τ IM ∈ [0; 1]: Collateralization level.σ (δ1): Standard deviation of δ1.f IM : Constant.

Variation marginsMeant to cover current exposure.

χVMji = τVM f VM · (δ1 − δ0)max 0;ωji

f VM : Constant.

Failures from collateral shortage (inability to post variation

margins) are ruled out through an additional constraint.


Model - Sequential trading problem

Rene notations:ωij : CDS contract currently being negociated between i and j .ωsij : sum of all (adding up or osetting) agreed-upon trades between i and j

before instant s.

Expected utility for i at date s when matched with j :

Vi (ωij , pij) =

∫ 1

0

π (δ1)

[λiU (0) + (1− λi)

[(1− δ1)U

(Ci + aiR + χi

)

+δ1

[ ∑Φ⊆Ω\i

∏k∈Φ

λk∏k /∈Φ

(1− λk) · U

(Ci

+∑k∈Φ

[−max 0; ωsik+ χki ]−

∑k /∈Φ

[ωsikR + χik ]

)]]]dδ1

Some simplifying notations have been introduced.More on notations.

Budget constraints are also updated with the trading process s.


Calibration

Banks

n = 5 banks (main dealers in one area).U: CRRA utility with elasticity of substitution γ = 0.3.Total bank assets drawn from a Power law distribution.Random assignement of shares β and (1− β) for ai and ci .Bank probabilities of default drawn from a beta distribution(support [0; 1]) calibrated from credit ratings.

Assets

r0 = 1.029 (10-Year U.S. Treasury Constant Maturity Rate)R = 1.158 (Long-term arithmetic average of S&P 500 return).

Collateral

f IM = 10 (Potential future exposure)f VM = 2 (Current exposure)


Outcome metrics

Restrict attention to key metrics.

Gross notional amount: Size of the market.

Multilateral net notional: Exposure at default

Net over gross ratio: Extent to which trading activity

generates exposure at default. Proxies for market liquidity.

Total collateral and collateral over net notional ratio:Counterparty risk mitigation.

Average volume-weighted price: Pricing of the contracts.


Results - Bilateral clearing, varying τ

Outcome metrics for changing collateralization levels on

bilateral trades.


Results - Bilateral clearing, varying τ

Gross market size shrinks by 21%, but net exposure decreasesto a lower extent (13%).

The net-over-gross ratio increases: Market liquidity /intermediary activity are lower.Some end-users no longer get credit risk protection.Thus, sizeable eects for both intermediaries and end-users.

Increased collateral requirements are priced: higher spreads

paid by CDS buyers.


Results - Rehypothecation

Rehypothecation: re-use of collateral.

Common practice on OTC derivative markets (Singh 2010)

Assume a fraction ρ ∈ [0; 1] of collateral received can be

rehypothecated.

At t = 0, rehypothecation of initial margins.



Outcome metrics with bilateral trades and changing

rehypothecation, τ IM = τVM = 1.



Rehypothecation increases gross market size by about 13.7%,but net notional remains unchanged.

The ability to rehypothecate does not increase the ability ofend-users to get credit risk protection.But intermediary activities increase to a large extent.

Collateral over net ratio drops (from 0.21 to 0.12).Policy debates on rehypothecation should weigh the costs andbenets of extensive collateralization and of well-developedintermediary activities.Trading volumes by end-users are not a rst-order concern.

Prices decrease slightly as rehypothecation increases.


Results - CCP clearing

Bilateral exposures satisfying a size criterion are novatedto a CCP.

All exposures above T have to be centrally cleared.Size criterion T can be interpreted as a proxy forstandardization.

Example: Novation of ωij < 0 to a CCP.

The CCP buys ωCCP,j = ωij from j .The CCP sells −ωCCP,j to i .

Multilateral netting of exposures novated to the CCP.

Collateral required by the CCP:

Full collateralization : τ IM = τVM = 1The CCP does not post initial margins.Default fund contribution: fraction ψ of initial margins.



Outcome metrics when increasing CCP clearing (reducing T )

Uncleared bilateral trades uncollateralized, τ IM = τVM = 0.



Eects very similar to those of increased bilateralcollateralization.

Gross market size decreases by 34.1%.Some end-users trade less in net termsNet over gross ratio increases from 0.52 to 0.66 (lower marketliquidity).Collateral demand increases to represent 18.2% of netexposures.Increased collateral requirements are priced.


Results - Calibrated example

Run an experiment with a calibration close to pre-reformparameter values.

Pre-reform case:

No central clearing.No bilateral initial margins.Variation margins τVM = 0.88 (ISDA 2013).Rehypothecation ratio ρ = 0.75 (ISDA 2013).

Post-reform case:

Full CCP clearing: T = 0.Default fund contribution ψ = 0.15 (Ra 2012).


Results - Calibrated example

Not accounting for dynamic eects may lead to an

over-estimation of system-wide collateral demand between

22% and 47%.


Extensions - Probabilities of default

Role of bank probabilitities of default : What if all bankprobabilities of default are driven up by an idiosyncraticfactor?

Benets of collateral posting are larger ceteris paribus.

Low impact of bank PD if full collateralization.


Extensions - Probabilities of default

Benets of central clearing are also larger ceteris paribus.Dierences due to counterparty risk almost vanish whencentral clearing is widespread.

Lower incentives to screen counterparties.


Extensions - Safe asset supply

Keep each bank size constant, reduce the proportion of safeassets.

Akin to the downgrade of safe assets (≈ safe assetshortage).Blue: base case, red: ÷2, green: ÷4.


Extensions - Safe asset supply

Large consequences on market size, in particular netexposures.

Portfolio rebalancing: Traders less willing to take on morecredit risk when risky assets are in larger supply.

Much higher net over gross notional ratio when the

collateralization level is high enough.

However, the collateral over net ratio decreases.

First-order eect on CDS prices, which increase

signicantly.


Conclusion

Dynamic model of OTC derivatives network formation.

Network is endogenous to collateralization and clearingrequirements.Idiosyncratic counterparty risk accounted for.Both prices and quantities are negociated.

Dynamic eects of collateral and clearing on OTCderivatives market size and structure are large.

Reduction in both market liquidity and access to the marketfor end-users.Between 22% and 47% over-estimation of collateral demand incase dynamic eects are not accounted for.Part of the costs of collateral and clearing are passed ontobuyers through higher prices.Sizeable consequences of a change in safe asset supply.


Further research

Model with multiple assets

Asset default correlation likely to play a role if initial andvariation margins are properly modeled.Benets from diversication

Robustness of simulated networks to contagion

Contagion when accounting for collateral and clearing.Quantify the risk-mitigating role of collateral.

Normative (welfare) analysis

Increased collateralization needs not be welfare-improving.Nature of CDS contracts that are no longer traded: truehedging needs or other trades?


Appendix - Notations in the sequential problem

Notations introduced in setting up the sequential problem.

Ci ≡

(ci − Ki − χi + ωijpij +

∑k

ωsikpik

)r0

Ki ≡ κ∑k

1Ξs(i ,k)=1

χi ≡ χIMi

(ωij +

∑k

ωsik

)+ χVM

i

(ωij +

∑k

ωsik , δ1

)χij ≡ χIM

ij + χVMij

Return.


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