collateralisation: cva & fva - murex - alexandre bon

The CVA Conference:

CVA & Liquidity Implementation Stream

March the 23Rd, 2012

London

OTC COLLATERALIZATION

Implementation Issues in

CVA & FVA Frameworks

Alexandre Bon

Copyright ® 2012 Murex S.A.S. All rights reserved

Preliminary remarks

Credit and Funding:

– Two sides of the same coin

– Inherently asymmetric and a portfolio level issue

Where is the risk-free asset?

What about the « Law of One Price? »

– Market equilibrium price

– close-out value

– profitability measure

Speed of innovation vs. financial engineering

entropy

2


Agenda

CSA clauses & variations

Modeling collateralized exposures: CVA vs. FVA

The Standard CSA: challenges and systems implications

A word on clearing

CVA/FVA organizational frameworks

3


Introducing the Collateral Agreement

A bit of terminology : Collateral, ISDA & CSA

– CSA : credit support annex

– Non-mandatory appendix to the ISDA master agreement (which enforces close-

out netting for eligible contracts)

– Defines the scope and terms of bilateral remargining agreement

– CSA is the most common (but not the sole) collateral agreement for OTC

derivatives

– Standard templates but varied implementations (differences in clauses and

jurisdictions)

Main clauses

– Eligibility of positions to close-out netting and collateralization

– Eligibility of pledge-able assets and applicable haircuts

– Remargining process : valuation, frequency, settlement, reconciliation, dispute

resolution

– Determination of the collateral balance: symmetry, thresholds, independent

amounts, minimum transfer amounts, rounding rules…

– Legal framework: pledge or title-transfer, rights of re-use & rehypothecation

– Remuneration of the collateral account (most often based on an OIS rate, but

not always!)

4


Collateralization & typical portfolio mix

An institution’s OTC portfolio will commonly contain a mix of:

– Bilateral CSAs with 0 threshold and daily margining (cash)

– Positions cleared on CCPs : daily or intraday exchange of Variation and

Initial Margin

– CSAs with asymmetric terms

• One-way with SSAs

• Over-collateralized agreements (IAs, Thresholds, IM) and security collateral (e.g.

PB agreements) : small funds and corporates

– No CSA

– Multiple “collateral sets” with a single credit entity (by products : CSA,

GMRA, OSLA, GMSLA … or entities)

Some local variations, but the interbank market is mostly on

bilateral CSAs and daily cash margining

Imperfect collateralization bears additional risks & and

warrants further valuation adjustments (credit and funding)

5


Modeling Credit Exposures

Monte Carlo Simulation:

– Generate thousands of risk factors paths across hundreds of time-points

– Revalue each transaction on each node

– Aggregate at each node the transactions MtMs taking into account credit risk

mitigants to get the counterparty’s portfolio value

– For each time step, take the histogram of Credit Exposures across scenarios to

derive Expected Exposure and Liability profiles (as well as PFE or other statistics)

Expected

Exposure

MtM1 (1)

MtM2 (1)

MtMN (1)

.

.

.

.

.

.

6


MC system implementation questions

Models & calibration choices are important

But do not underestimate the other big issues:

Data Quality & Flows

System(s) interoperability issues

Evolution and maintenance

7


CVA - Collateral Modeling

MarginingNodes

Netting NodesCounterparties

Bank ABC

ISDA - ABC

CSA

No collateral

GMRA GMRA

No netting No collateral

Eligibility rules

Exposures are

mapped to Netting

and Margining sets

Upon close-out the

collateral balance

is offset against

the netting node

positions

8


CVA - Collateral Modeling

Exposure at t is the difference of the Close-Out value of the portfolio

and Outstanding collateral balance

Considering the simulation date correspond to the close-out date

following default one identify the previous effective re-margining date

Common modeling options

close-outgrace

perioddispute fail

previous

remargining

Simulation

date Ti

Simulation

date Ti-1

Unsecured exposure

(collateralised set)

Collateral Balance

Margin Period of Risk

Ti - MPR

Exposure

Threshold

9


Stylized example with Currency Swaps

CCS vs. FX reset swap

FX reset swap has an inbuilt

collateralization feature

Market risk : low FX Delta for

the FX reset swap

11




Impact of collateralization on

the CCS risk (10 days MPR)

12




FX reset swap exhibits slightly

larger collateralized exposures

and liabilities, due to larger CF

settlements.

Margining-square not a

desirable feature

Side-note : collateralization is a

great hedge

– CCS Bilateral CVA drop of 60%,

– FX delta and DV01 near 80%,

CR01 near 80%

The case for simple upfront

reserving for collateralized

exposure, vs. dynamic hedging

of non collateralized exposures.

13




Impact of reduced re-margining

frequency (1 week to daily)

14


CVA – Collateralization Efficiency

Main collateralization risks and issues:

Lack of standardization across CSAs

Costs and risks of operation (bilateral & 0-threshold)

Concentration risk

Credit dependent clauses

Eligibility of collateral assets & haircuts

Execution : rounding, split differences, disputes

– In practice collateral amount will never exactly match the exposure

levels

– The former are typically ignored in the model, the latter managed by

adjusting the MPR of problem counterparties (dispute history).

Rehypothecation and re-characterization risks

Gap Risk

– Model risk & close-out value

– JTD & Wrong way risk

16


One-Way Collateral Agreements

Sovereigns, Supranationals and Agencies (SSAs)

Small non-bank counterparties without a collateral

management function

Potentially large exposures for the un-collateralized

party

Bilateral CVA ~ Unilateral CVA

Exposures vs. Liabilities distributions

Part I

17


Collateral gap risk

Instantaneous jump in exposure and counterparty default

leaving a portion of the portfolio un-collateralized

• More prevalent with imperfect CSAs

(large thresholds & MTAs, longer remargining frequencies)

• Credit protection bought from related entity

• Simply settlement effects (warrant special treatment?)

• Liquidity effects upon counterparty default

18


Rehypothecation

Rehypothecation:

– The collateral taker uses pledged assets as security for his own obligations to a third

party

Right of re-use:

– Covers rehypothecation as well as any use of the collateral asset in line with

ownership of the property (e.g. sale, lending to a third party)

Depending on the jurisdictions and legal phrasing, collateral

exchange can be performed under:

– A Title Transfer Arrangement (implicit re-use rights)

– A Pledged Collateral Agreement, where the rehypothecation right may be explicitely

granted (often the case with non-bank counterparties)

Similar question with cash collateral and margin segregation

Some remarks:

– Rehypothecation and “re-pledging chains” have played an essential part in providing

liquidity (and leverage) to the financial markets

– The GFC showed how damaging the combined effects of reduced collateral velocity

(cf. Lehman close-out) and collateral squeeze (haircuts) can be in a systemic shock.

– Not a desirable feature from a CCR mitigation point of view, but forfeiting this right

represents a funding cost.

19


Risk-free or risky close-out

ISDA documentation not 100% clear on how we

should price the liquidation value of derivatives.

Open issue for default close-out as well as

valuations for Unwinds and ATEs

Introduces a recursive pricing issue

Theoretical justifications for both approaches: the

need for another Valuation Adjustment

(RVA/ATEVA) ?

Practical questions:

– Pricing of DVA or funding cost in distressed markets

– Joint-default

– Going-concern collateral balance is determined based on risk-free

valuation

20


From Credit to Funding

Valuation

Calibration

DiscountingCredit risk

21


Funding benefit & funding cost

Classical pricing models assume that we can borrow/lend at a

risk-free rate.

Post crisis, financial institution fund with significant spreads.

– This credit/liquidity component appears in LIBOR basis spreads (OIS/LIBOR

and LIBOR of different tenors)

OIS vs. LIBOR 3M spread


Funding un-collateralized trades

In any derivatives contract future cash-flow exchanges need to

be “funded”.

A bilateral position with an open negative MtM can be seen as an

overnight loan granted by the counterparty : logically this funding

benefit is financed at our cost of funds.

A positive MtM represents a funding cost : by unwinding the trade

and investing this amount with my treasury (or buying back my

own bond issue) I could get the same rate.

Hence an uncollateralized transaction’s Cash Flows should be

discounted at my senior unsecured cost of debt.

Neglecting the CDS-Bond basis, my senior unsecured cost of funds

is in line with the assumptions PDs and Recovery of the CVA

calculation. Hence at a single contract level (i.e. single deal or

netting set): DVA = Funding Benefit.

23


Funding cost: the (non-)effect of netting

In practice whether a set of

transactions is covered by a

close-out netting provision

(ISDA) or not, has no implication

on their funding cost (and thus

the discounting curve to be used)

For non-fully netted portfolios the

Funding Benefit is not equal to

DVA!

– No close-out netting agreement

– Multiple netting sets

2 parties A & B have two exactly offsetting trades but no

netting agreements between them:

– Both parties will have non-zero CVA & DVA terms (and bilateral CVA)

– They both have 0 funding cost as CFs will offset.

24


Funding collateralized trades

If a CSA is in place, the “lender” typically receives a collateral

for a value ~ equal to the MtM of the position, either as:

– a Cash amount, which can be re-invested (overnight) and on which a pre-

specified interest is paid back to the poster (typically compounded OIS

index).

– a Security. If the CSA agreement allows for re-hypothecation, that collateral

can be repo-ed to another party to fund at a much lower rate than an

unsecured funding rate.

– Simplifying assumptions: 0 Thresholds & MTAs, daily remargining, one

currency, no haircuts on securities, no dispute…

Hence CSA-covered positions can be funded by using an OIS

discount curve

Non CSA-covered positions are funded using the internal cost

of funds (senior unsecured debt)

25


The Ideal CSA Hypotheses

Bilateral Agreement

Continuous Margining

Instantaneous settlement of margin calls

0 Threshold and Minimum Transfer Amount

No Independent Amounts

No haircuts

Cash (or equivalent instrument) collateral, independent from exposure

No valuation differences

No disputes

Netting set = Margining set

No Initial Margin

CCR :

– No rehypothecation / segregation of collateral accounts

– No posting of Initial Margin with risky entities

– No settlement risk on margin flows

Funding :

– Rehypothecation / no segregation of collateral accounts

– No posting of Initial Margin

– Single risk-free collateral asset (e.g. no currency basis arbitrage)

26


New FO and Risk systems needs

Front-Office systems require flexible curve allocation

mechanisms:

– Collateral documentation is pricing data!

– Rule-based dynamic allocation of curves based on both the leg currency and underlying

collateral currency

Proper allocation of risk and sensitivities

– E.g. Uncollateralised CMS swap (CMS rate derived from collateralised instruments)

Need a multiple curve calibration engine:

– Able to detect the

dependencies

– Wider selection of curve

building instruments

– Simultaneous bootstrapping of

all involved curves with

accuracy and speed.

27


Pricing example

In-the-money XCCY

swap EUR/USD with 5Y

outstanding maturity

P&L impact of 36bp

Forward MtM, vs.

Expected Exposure &

Expected Liability

evolution.

Uncollateralized USD CSA

28


Pricing in a Multiple Curve Environment

Forwarding curves are derived from collateralized quotes

– Joint bootstrapping of discounting and forwarding curves

– E.g. EONIA and EURIBOR 3M, then EURIBOR 6M vs. 3M…

– Triangular calibration with XCCY basis curves or markets with varying liquid swap

tenors depending on the horizon.

Different discounting curves depending on the CSA clauses.

– EURIBOR swap collateralized in EUR is discounted on an EONIA curve

– EURIBOR swap collateralized in USD is discounted on a EUR/USD XCCY basis curve

built upon a USD Feds Funds curve.

29


Pricing in a Multiple Curve Environment

Pricing of Exotics requires multi-curve

evolutions for pricing of exotics and CVA

estimation.

– Current standard market practice: deterministic basis spreads

curves on top of a risk-free OIS curve

– Currently testing a HJM 2F stochastic basis spread model,

calibrated to historical data (results to be presented soon).

Another difficult question pertains to

correlations

(OIS-LIBOR spread vs. rates, bond-CDS basis vs. LIBOR basis and

credit…)

30


Limitations of the deterministic spreads view?

31

Even plain vanilla swaps require several curves to be priced

Using deterministic spreads obviously implies a perfect correlation

between various curves used in the model.

Is such a constraint acceptable, in light of recent market changes ?


Empirical tests on recent data showed that:

– Deterministic spreads are a decent approximation when pricing

collateralized callable fix-float swaps (reassuring for CVA)

– However for basis products both the spread volatility correlation

between rate curves have a significant impact on the valuation

32

Limitations of the deterministic spreads view?


Main issue: the CSA is not perfect

When exposure is in-between thresholds, we fund at

LIBOR + spread and not at OIS flat

Non-cash asset: haircuts and rehypothecation rights?

Choice of collateral currency:

– E.g. steep XCCY basis spreads with the 2011 EOY USD squeeze

– Apparently comparable to a contingent Bermudan XCCY swaption on

the portfolio (hint at American Monte Carlo pricing)

– In practice varying implementation approaches

– However, uncertain execution / enforceability

• Different legal interpretations (US vs. UK law – do we require the consent of

the receiving party? Is full substitution always possible when there is no

margin call?...)

• Will the collateral management team deliver the adequate collateral?

– Will the issue disappear with the Standard CSA?

Does the local market even have a liquid OIS instrument?

One-way CSA case is another tricky case of funding

asymmetry (one threshold pushed to infinity)

33


One-Way Collateral Agreements

Funding cost at OIS flat

Funding benefit at unsecured debt level

Double hit: CVA & FVA

Usually SSAs will have much lower credit spreads than the institution so

the Funding risk effect would dominate the Credit risk one.

Difficult to value in the simple discount switch setting,

however actual quoted price is unlikely to be the “fair-one”.

Receive funding at OIS flat

Borrow at LIBOR + spread

Part II

34


Introducing the Standard CSA

New collateral support annex protocol promoted by

ISDA

Aim to standardize valuation practices

– Specify OIS discounting

– Remove the collateral switch optionality

– Align CSA to the margining mechanics of CCPs

0 Threshold, no MTA, daily margining

Cash collateral only for variation margin

Phased implementation in 2012 : transactions can

be moved from legacy CSA to S-CSA

Transactions pooled in 5 Designated Collateral

Currency buckets

35



CHF trades

CHF collateral balance

EUR trades

EUR collateral balance

GBP trades

GBP collateral balance

JPY trades

JPY collateral balance

CCS and other

currencies

USD collateral balance

Local currency OIS discounting

(EONIA, SONIA…)

Discounting on USD

Feds Funds & corresponding

FX basis curves

Phase I

Margin

Calls / Deliveries

Counterparty

Herstatt Risk!36



CHF trades

CHF collateral balance

EUR trades

EUR collateral balance

GBP trades

GBP collateral balance

JPY trades

JPY collateral balance

CCS and other

currencies

USD collateral balance

Phase II

Margin

Calls / Deliveries

Safe settlement: PvP platform operated by ISDA

Swap margins to USD (ISA method)

Counterparty

37


Moving to S-CSA: system implication

MarginingNodes


Bank ABC

ISDA - ABC

Legacy CSA

CSA – EUR

…

CSA – USD*

No collateral

…

Straight-forward

adaptation of the

CVA Monte Carlo

Engine thanks to

dynamic

construction of the

netting and

margining sets

(rule-based)

In practice, need

to follow closely

migration of trade

blocks (by

products, entities)

from legacy CSA to

SCSA margining.

38


S-CSA implementation challenges

Collateral systems impact:

– Electronic messaging

– Exposure pooling and collateral accounts by currency buckets & flexible

mechanism to migrate positions off legacy CSA

– Mandatory OIS discounting

– Implementation of ISA & PvP processes

Front-office:

– Availability of collateral eligibility criteria at point of pricing

– Discount curve allocation mechanism based on CSA / SCSA mappings

– For a period of time maintain local OIS curves and Basis OIS curves

CVA / FVA units

– Consistent mapping of the positions to currency buckets

– Multiple margining sets per netting set

– Value margin conversion via ISA-type method and capture FX risk over

MPR

ISDA : “Regardless of approach, firms will need to undertake considerable internal

technology and process re-engineering work to implement the SCSA.”

39


FVA - Collateral Modeling

An alternative approach to the Discount Method consists in

looking at the question from a portfolio level by representing the

funding cost as another valuation adjustment(the OIS curve providing a proxy for the risk-free rate).

Evolve market rates and explicitly model the collateral balances

and a funding strategy. E.g.

– Collateral balance : funded at OIS flat

– Portfolio value – balance : shortfall funded at own cost of funds

Extend existing CVA simulation framework since this will provide:

– A consistent pricing framework for CVA and FVA (calibration, deal aging and termination

events)

– The CVA engine already has all required business logic (margining set mapping, curve and

spreads evolution)

– A validated & controlled infrastructure : inter-system data flows, interfaces, reconciliation

processes

– A low & managed TCO, as one can leverage existing infrastructure (e.g. grid, GPU farm) :

running FVA calculations on top of a CVA simulation is computationally efficient (provided i.

consistent modeling assumptions and ii. that collateralised positions are already included)

40



Rates curves are

evolved jointly

Collateral

Balances are

obtained at the

margining node

level

Collateral assets

are funded at the

Agreement’s

specified rate

source

Collateral

shortfalls funded

on funding curve

MarginingNodes


Bank ABC

ISDA - ABC

Legacy CSA

CSA – EUR

…

CSA – USD*

No collateral

…

41



Practical simulation implementation : DVA is not the FVA

benefit (MPR vs. Settlement lag).

Simulation

date Ti

Simulation

date Ti-1

Collateral Balance (CVA)

Margin Period of Risk

Ti - MPR

Settlement

Lag

Ti - SL

Collateral Balance (FVA)

Collateral

Funding

42



Reducing the MPR (10 days)

to the Settlement lag (3

days) halves the DVA

estimate.

Final FVA impact would be

stronger on portfolios with

imbalanced EPE/ENE profiles

or asymmetric collateral

terms (thresholds, IAs, one-

way CSA).

43


Managing consistently Funding & Credit

Stating the obvious: need consistency between valuation practices &

business models

Collateral optimisation, transformation

Funding vs. liquidity

Hedgeable costs vs. friction and cost of doing business

45

Credit Funding

Collateral


Managing consistently Funding & Credit

Discount curves approach vs. Global revaluation model

Asymmetric or symmetric FVA expression:

– As a funding cost

Risky Value = Risk-free Value – CVA + DVA – FCA*

– As a funding adjustment

Risky Value = Risk-free Value – CVA + FVA

System implementation

– The same simulation can provide DVA and FVA broken down in FCA & FBA

– DVA can be computed as mandated by FAS157 (topic 820) / IFRS 13

– FVA can be outsourced to and hedged by a dedicated CFU

– CVA desk can hedge unilateral CVA or unilateral CVA + DVA-FBA basis

– FO incentivization through marginal pricing

Basic modeling and implementation questions:

– Credit Liability does not have to coincide with the amount to fund (non-

netted trades, netting set fragmentation)

– Margin Period of Risk adjustment vs. Settlement Lag

– CDS – Bond basis spread46


Modeling framework vs. Mandates

Model choices, system parameterization should

be made with their users mandates in mind

– Risk management vs. CVA desk vs. Funding

– Minimizing accounting P&L volatility, JTD risk, Liquidity risk,

Funding costs, and/or capital requirements

– Incentivizing risk-takers

– Active hedging (of which components?)

Some obvious impacts

– Choices of metrics, data inputs, adjustments

– WWR, basis and cross-gammas

– P&L management tools

– Fees management, data workflows, systems interoperability

47


What about FVA for CCP-cleared products?

Margin requirement broadly split in IM and VM

IM typically large and aimed at covering gap risk over the

auctioning period (so as to preserve default funds contributions)

IM models are typically VaR-based (adjusted with credit and

liquidity factors)

The IM funding requirement will then depend on the

“directionality” of the cleared portfolio!

Should this additional cost be modeled on an incremental basis

(consistent with CVA and OTC FVA), or handled as a post trade

operational cost? Incentives may differ depending on the

institution.

Extending the CVA/FVA model to provide estimation of forward

Initial Margin requirements would require a forward approximation

of the margining sets VaR. Computationally, the issue is similar to

the estimation of the incremental RWA cost of capital.

48


Variation Margin and Initial Margin

FVA for cleared products should, in theory, account for the

incremental cost of funding of the Initial Margin

High C.L.

VaR

Position at Ti-1 Position at T

5 days to close the auctioning process

Variation Margin

Initial Margin

49


Questions and practical issues

Vanillas are de-facto level-2 derivatives and market prices are not

transparent (difficulty to unwind off-market positions)

Broker quotes need to be reinterpreted (e.g. B&S vols)

New premium quotation modes (unfortunately not applicable for all

types of options)

Sensitivities and hedge ratios differ between collateralized and

uncollateralized cases

Perfect hedge can only be achieved under identical collateralization

terms

Pricing effects are complex to quantify for imperfect

collateralization cases and embedded optionalities

Difficult /costly hedging of basis risks

Convexity and wrong-way effects deemed small (valuation impact

smaller than bid-ask) but traders need to be aware of them

Which CSA clauses should be modeled / can be hedged ?

50


Questions and practical issues

Internal organization challenges:

Need to implement consistent pricing of new transactions, unwinds

and legacy books

Fair pricing of internal positions

Ownership of the funding issue and hedging

Ensure that the Collateral Management & Treasury functions

provide optimal funding (as supposed in the pricing)

Integration of data flows and inter-operability : both a processes

and systems challenge !

Establish clear-cut transfer pricing and cost management policies

51


Two modeling and organizational models

Discount curves method Global FVA/CVA exposure method

Requires significant investments (starting with

a simulation framework)

Global hybrid pricing consistent across desks

and with CVA.

Flexible handling of CSA agreements and

explicit modeling of the funding strategy

– Reproduces the previous method results under

specific case

– Can include funding impact of credit mitigants

Isolates clearly funding cost from valuation and

CVA

Portfolio-level, cost reallocated to the trades

(like CVA)

Funding and convexity risk transferred to a

centralized Funding / Treasury desk

Works best when bringing together Treasury,

CVA and Collateral trading operations

Simpler to implement in a crude way,

additional complexity with curves

management and FO assignments

Trade level pricing compatible with local

models.

Fail to account for corner cases

– asymmetric funding terms

– convexity effects (e.g. spread / rates correlation)

– liquidation value at risky value

Non-explicit link with DVA

Deal-level and easily understood by traders

Funding and convexity risk owned by the

traders

Works best with smaller decentralized

operations well collateralized

Open question : what should be the regulatory treatment of the FVA market risk in the

second setting? FVA VaR integrated in the IMA model?

52


Some useful references

Collateralization & Counterparty Risk:

D. Brigo & A. Pallavicini (2011) – Arbitrage-Free Counterparty Risk Valuation

under Collateral Margining

D. Brigo (2011) – Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout,

Netting, Collateral, Re-Hypothecation, WWR, Basel, Funding, CCDS and Margin

Lending.

J. Gregory (2009) – Being two-faced over counterparty risk

J. Hull & A. White (2011) – CVA and Wrong Way Risk.

ISDA (2011) – Overview of ISDA Standard Credit Support Annex (SCSA).

M. Pykhtin (2010) – Collateralised credit exposure, in Counterparty Credit Risk,

edited by E. Canabarro, Risk Books.

M. Pykhtin & D. Rosen (2010) – Pricing Counterparty Risk at the Trade Level and

CVA Allocations.

Books:

G. Cesari & al. – Modelling, Pricing, and Hedging Counterparty Credit Exposure.

J. Gregory – Counterparty credit risk – The new challenge for global financial

markets. Wiley Finance.

53


Some useful references

Collateralization & Funding:

C. Burgard, M. Kjaer (2011) – In the Balance.

C. Fries (2010) – Discounting Revisited: Valuation Under, Funding, Counterparty

Risk and Collateralisation.

M. Fuji, Y. Shimada & A. Takahashi (2010) – Collateral Posting and Choice of

Collateral Currency.

A. Green (2011) – Engineering a CVA and FVA solution, talk given at the WBS

Discounting and Funding conference, November.

D. Loiseau (2012) – Introducing Stochastic Spreads in a Multi-Curves Framework,

Murex talk given at the MathFinance Conference, March.

M. Morini & A. Prampolini (2010) – Risky funding: a unified framework for

counterparty and liquidity charges.

V. Piterbarg (2010) – Funding beyond discounting: collateral agreements and

derivatives pricing, Risk Magazine, February issue.

Risk Magazine (2011) – The evolution of swap pricing. Nick Sawyer, March issue.

M. Singh & J. Aitken (2010) – The (sizable) Role of Rehypothecation in the

Shadow Banking System.

54

T H A N K Y O [email protected]

55

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collateralisation: cva & fva - murex - alexandre bon

Economy & Finance

currency swaps

senior unsecured

deterministic

references

deterministic

collateral

collateral

margining