OTC Collateralisation : implementations issues in the context of CVA & FVA
- The ideal CSA hypothesis : Imperfect collateralisation for credit mitigation and/or funding
- FVA vs. CSA-discounting
- Implications in terms of curves calibrations and management
- FVA for Cleared positions
- FVA or CSA-discounting : which funding management model?
2. 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
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2
3. 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
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3
4. Introducing the Collateral Agreement
A bit of terminology : Collateral, ISDA & CSA
–
–
Non-mandatory appendix to the ISDA master agreement (which enforces closeout 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
–
CSA : credit support annex
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!)
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4
5. 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)
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5
6. 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)
MtM1 (1)
MtM2 (1)
.
.
.
.
.
.
Expected
Exposure
MtMN (1)
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7. 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
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7
8. CVA - Collateral Modeling
Counterparties
Netting Nodes
Margining
Nodes
Eligibility rules
CSA
Exposures are
mapped to Netting
and Margining sets
Upon close-out the
collateral balance
is offset against
the netting node
positions
ISDA - ABC
No collateral
Bank ABC
GMRA
GMRA
No netting
No collateral
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8
9. 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
Margin Period of Risk
previous
remargining
dispute
fail
grace
period
close-out
Unsecured exposure
(collateralised set)
Exposure
Collateral Balance
Simulation
date Ti-1
Threshold
Simulation
date Ti
Ti - MPR
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10. 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
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11. Stylized example with Currency Swaps
CCS vs. FX reset swap
Impact of collateralization on
the CCS risk (10 days MPR)
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12
12. Stylized example with Currency Swaps
CCS vs. FX reset swap
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
–
–
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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
13. Stylized example with Currency Swaps
CCS vs. FX reset swap
Impact of reduced re-margining
frequency (1 week to daily)
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14
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
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16
15. One-Way Collateral Agreements
Part I
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
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17
16. 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
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17. Rehypothecation
Rehypothecation:
–
Right of re-use:
–
The collateral taker uses pledged assets as security for his own obligations to a third
party
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.
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19
18. 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
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19. From Credit to Funding
Credit risk
Discounting
Calibration
Valuation
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20. 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
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21. 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.
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23
22. Funding cost: the (non-)effect of netting
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.
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
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23. 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 prespecified 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)
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24. 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 posting of Initial Margin with risky entities
–
No rehypothecation / segregation of collateral accounts
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)
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26
25. 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:
–
–
Wider selection of curve
building instruments
–
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Able to detect the
dependencies
Simultaneous bootstrapping of
all involved curves with
accuracy and speed.
27
26. Pricing example
Uncollateralized
USD CSA
In-the-money XCCY
swap EUR/USD with 5Y
outstanding maturity
P&L impact of 36bp
Forward MtM, vs.
Expected Exposure &
Expected Liability
evolution.
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28
27. Pricing in a Multiple Curve Environment
Forwarding curves are derived from collateralized quotes
–
–
E.g. EONIA and EURIBOR 3M, then EURIBOR 6M vs. 3M…
–
Joint bootstrapping of discounting and forwarding curves
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.
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29
28. 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…)
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30
29. Limitations of the deterministic spreads view?
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 ?
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30. Limitations of the deterministic spreads view?
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
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31. 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)
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32. One-Way Collateral Agreements
Part II
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”.
Borrow at LIBOR + spread
Receive funding at OIS flat
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34
33. 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
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35
34. Introducing the Standard CSA
Phase I
Discounting on USD
Feds Funds & corresponding
FX basis curves
Local currency OIS discounting
(EONIA, SONIA…)
CHF trades
EUR trades
GBP trades
CHF
collateral
balance
EUR
collateral
balance
GBP
collateral
balance
JPY trades
JPY
collateral
balance
CCS and
other
currencies
USD
collateral
balance
Margin
Calls / Deliveries
Counterparty
Herstatt Risk!
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36
35. Introducing the Standard CSA
Phase II
CHF trades
EUR trades
GBP trades
CHF
collateral
balance
EUR
collateral
balance
GBP
collateral
balance
JPY trades
JPY
collateral
balance
CCS and
other
currencies
USD
collateral
balance
Margin
Calls / Deliveries
Safe settlement: PvP platform operated by ISDA
Swap margins to USD (ISA method)
Counterparty
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37
36. Moving to S-CSA: system implication
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.
Counterparties
Netting Nodes
Margining
Nodes
CSA – EUR
ISDA - ABC
…
CSA – USD*
Bank ABC
Legacy CSA
…
No collateral
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38
37. S-CSA implementation challenges
ISDA : “Regardless of approach, firms will need to undertake considerable internal
technology and process re-engineering work to implement the SCSA.”
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
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39
38. 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)
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40
39. FVA - Collateral Modeling
Rates curves are
evolved jointly
Counterparties
Netting Nodes
Collateral
Balances are
obtained at the
margining node
level
Collateral assets
are funded at the
Agreement’s
specified rate
source
Margining
Nodes
CSA – EUR
ISDA - ABC
…
CSA – USD*
Bank ABC
Legacy CSA
…
Collateral
shortfalls funded
on funding curve
No collateral
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41
40. FVA - Collateral Modeling
Practical simulation implementation : DVA is not the FVA
benefit (MPR vs. Settlement lag).
Margin Period of Risk
Settlement
Lag
Collateral
Funding
Collateral Balance (FVA)
Collateral Balance (CVA)
Simulation
date Ti-1
Ti - MPR
Ti - SL
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Simulation
date Ti
42
41. FVA - Collateral Modeling
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, oneway CSA).
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43
42. Managing consistently Funding & Credit
Credit
Funding
Collateral
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
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45
43. 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 (nonnetted trades, netting set fragmentation)
– Margin Period of Risk adjustment vs. Settlement Lag
– CDS – Bond basis spread
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46
44. 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
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47
45. 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.
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48
46. Variation Margin and Initial Margin
FVA for cleared products should, in theory, account for the
incremental cost of funding of the Initial Margin
5 days to close the auctioning process
High C.L.
VaR
Initial Margin
Variation Margin
Position at Ti-1
Position at T
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49
47. 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 ?
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50
48. 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
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51
49. Two modeling and organizational models
Discount curves method
Simpler to implement in a crude way,
additional complexity with curves
management and FO assignments
Trade level pricing compatible with local
models.
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
Fail to account for corner cases
–
asymmetric funding terms
–
convexity effects (e.g. spread / rates correlation)
–
Global FVA/CVA exposure method
–
liquidation value at risky value
Reproduces the previous method results under
specific case
–
Can include funding impact of credit mitigants
Non-explicit link with DVA
Isolates clearly funding cost from valuation and
CVA
Deal-level and easily understood by traders
Funding and convexity risk owned by the
traders
Portfolio-level, cost reallocated to the trades
(like CVA)
Works best with smaller decentralized
operations well collateralized
Funding and convexity risk transferred to a
centralized Funding / Treasury desk
Works best when bringing together Treasury,
CVA and Collateral trading operations
Open question : what should be the regulatory treatment of the FVA market risk in the
second setting? FVA VaR integrated in the IMA model?
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52
50. 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.
Copyright ® 2012 Murex S.A.S. All rights reserved
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51. 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.
Copyright ® 2012 Murex S.A.S. All rights reserved
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