Weitere ähnliche Inhalte Ähnlich wie Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA Discounting ? (20) Kürzlich hochgeladen (20) Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA Discounting ?1. Did Basel put the final nail in the coffin of
CSA Discounting ?
Amsterdam - May 15th, 2014
Alexandre Bon, Murex
FVA in presence of imperfect collateralisation, IMs and variable funding spreads
2. Copyright © 2014 Murex S.A.S. All rights reserved2
Introduction
Funding issues & FVA are all over the news
Institutions recently deciding to include FVA in their Financial Statements
Heated debates aroundValuation Adjustments
Funding troubles for Asian Banks on CNYTARFs products sold to corporates
2007-2009 : birth of the CSA discounting argument
Since then, major regulatory initiatives have been reshaping OTC derivatives markets:
Mandatory Clearing (Dodd Frank, Emir)
Upcoming regulation of CSAs for “non centrally cleared derivatives”
Higher costs of capital (LCR, NSFR, CVA charge…) and focus on asset optimisation (balancing capital and
collateral management needs)
As a result, the question is whether pricing approaches that have been implemented
after the GFC are still valid, or whether corrective adjustments are required:
Where funding costs matter most: uncollateralised corporate portfolios, one-way CSAs with SSAs,
Centrally cleared portfolios
Given “New Normal” market dynamics : e.g. spread volatility and correlation with other factors
3. Agenda
1. INTRODUCTION : FVA AND COLLATERALISATION
2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION
3. FUNDING SPREADS VOLATILITY
4. COLLATERALISATION REGIMES & INITIAL MARGINS
4. Copyright © 2014 Murex S.A.S. All rights reserved4
Cost Accounting vs. Financial Accounting analogy
Why compute valuation adjustments?
Initial motivation: incentivize risk takers by valuing all economic costs/benefits to the BU ignored
in the theoretical price (credit, funding, capital…).
Later on: recognize that market prices deviate from their theoretical levels (since institutions
adjust their quotes for CVA/FVA…) to present an accurate picture of assets values in financial
statements.
Cost Accounting: aims at presenting detailed costs information to feed in internal
managerial decisions and control current operations by optimally allocating resources to the
most efficient and profitable business areas.
Financial Accounting: produces formalized financial statements (P&L account and Balance
Sheet) that are used by external stakeholders to get a “true and fair” picture of transactions,
and analyze the results and financial position of the firm on a given date.
5. Copyright © 2014 Murex S.A.S. All rights reserved5
Cost Accounting vs. Financial Accounting analogy
Cost Accounting
Internal reporting, Forward looking
Costs classified as fixed, variable, semi-
variable, but also by product, process, BU…
E.g. marginal costing approach:
Cost per unit ascertained only on the basis of
variable costs
Fixed costs are excluded from the product cost
and charged as period costs to the P&L of the
BU cost center.
Stocks are valued at marginal cost of production
Financial Accounting:
External reporting, Backward looking
Costs classified by conventional transaction
categories
Valuation approach & reporting:
Unit of account vs. unit of valuation
Conventional by definition
Should follow a symmetry principle (i.e. for
valuation adjustments one firm’s cost is its
counterparty’s benefit)
Proposal for this presentation
Management of EconomicValue :
focus on incremental impact of new operations (trades, unwinds, extensions, roll-out of new CSA…)
only include variable costs in the value adjustment at operations level, manage fixed costs as reserves at the BU level
and set profitability target to cover those.
Financial reporting: market transfer price based of conventional assumptions (e.g. market funding levels, HTM)
6. Copyright © 2014 Murex S.A.S. All rights reserved6
CVA & FVA definition
CVA & DVA
CVA is the market value of counterparty credit risk for OTC derivatives (or the difference
between the risk-free price and the mid-market price of the portfolio).
Expectation over time of discounted future exposures weighted by default probabilities and
recoveries.
FVA
Similarly FVA aims to capture the funding costs (FCA) and benefits (FBA) incurred on derivatives
transactions due to timing mismatches between inflows and outflows that would be financed at
unsecured rates.
Integral over time of Funded Amounts weighted by the corresponding Funding Spreads.
As funding spreads contain a credit risk element and funded amounts can correspond (not
always) to discounted exposure, there are definite overlaps between bilateral CVA and FVA (esp.
FBA and DVA).
7. Copyright © 2014 Murex S.A.S. All rights reserved7
Justification for a funding adjustment
Case of an unsecured derivatives transaction
Future cash flow assets (liabilities) are term-funded by investing (borrowing) in a “risk-free”
money market account that will pay back the required amount.
Since there is no derivatives repo market, the amount to be invested in the cash account needs
to be borrowed (lent) on an unsecured basis.This is done theoretically through Treasury by
issuing (buying back) zero-coupon bonds maturing on the cash flows value dates.
Since derivatives cash-flows are stochastic the position in the zero-coupon bond (i.e. CFs’ NPV)
is re-balanced continuously.
i.e. the value of this derivative can be obtained by :
Discounting future cash-flows on our own unsecured funding curve (term-funding), as established by the
Treasury unit.
Equivalently, by taking the integral of future MtMs discounted with our unsecured funding spread over the
money market reference we get valuation adjustment that can be subtracted from the “risk-free” price to
derive our economic value for this transaction
In this second case splitting MtMs into Expected Exposures and Expected Liabilities let us define a funding
benefit (FBA) and funding cost (FCA) components (giving us the option to apply differentiated rates for
lending & borrowing).
8. Copyright © 2014 Murex S.A.S. All rights reserved8
Justification for a funding adjustment
Case of an unsecured derivatives transaction (continued)
So, assuming that:
our unsecured cost of funds is directly derived the price our Bond,
there is no CDS-Bond basis,
and that all transactions are done with a single counterparty, under one close-out netting agreement but no
collateral agreement,
we have DVA = FBA
(so this rarely is exactly the case in practice).
Other argument : the unsecured derivatives is hedged by a collateralized one
Some may argue that the funding requirement on day-one is not “real” as there are no flows yet
but if the transaction is hedged back-to-back with a counterparty with whom we have a perfect
CSA, posting (receiving) collateral covering the outstanding MtM will generate the same funding
requirement to source the collateral asset.
As we will see later, using this definition to define what the economic FVA of a trade should be,
might raise questions when the market standard collateralisation mechanics deviate from the
ideal case.
9. Copyright © 2014 Murex S.A.S. All rights reserved9
Justification for a funding adjustment
Case of a collateralised derivative position
When the value of the position 𝑉(𝑡) is positive we effectively borrow the collateral
amount 𝐶(𝑡) at the collateral rate 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 + 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 and fund the remaining shortfall
excess 𝑉 𝑡 − 𝐶 𝑡 at our cost of funds (and vice versa).
The collateral rate is the interest rate specified in the agreement, when exchanging
cash collateral (potentially in a different currency than the position’s), the funding
cost/benefit is thus the combination of:
𝑉 𝑡 − 𝐶 𝑡 +
at the unsecured borrowing spread 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤
𝐶 𝑡 − 𝑉 𝑡 −
at the unsecured lending spread 𝑆𝑙𝑒𝑛𝑑
𝐶(𝑡) at the collateral spread 𝑆𝑐𝑜𝑙𝑙𝑎𝑡
Assuming continuous collateralisation 𝑉 𝑡 = 𝐶(𝑡) : cash flows can be discounted on
the collateral rate
Usually the collateral rate is an OIS index which is also the benchmark for repos and
our “risk-free” money market account.
Under these ideal hypotheses : FVA = 0
10. Copyright © 2014 Murex S.A.S. All rights reserved10
Justification for a funding adjustment
Case of a collateralised derivative position (continued)
When posting securities as collateral:
with Rehypothecation allowed:
we pay the agreed collateral rate on C(t), but effectively receive
𝐶(𝑡)
1−𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡
that can be
repo-ed out for 𝐶 𝑡
1−𝑅𝑒𝑝𝑜 𝐻𝑎𝑖𝑟𝑐𝑢𝑡
1 −𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡
to earn the market repo rate: 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 + 𝑆 𝑟𝑒𝑝𝑜
giving rise to a funding benefit / cost as soon as 𝑅𝑒𝑝𝑜 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 ≠ 𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡
or 𝑆𝑟𝑒𝑝𝑜 ≠ 𝑆𝑐𝑜𝑙𝑙𝑎𝑡
without Rehypothecation rights:
When posting collateral we still receive 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 on 𝐶(𝑡)
When receiving 𝑋% of the collateral balance in securities we still need to fund
𝑉 𝑡 − 𝐶 𝑡 . (1 − 𝑋%) +
at our funding cost 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤 generating a funding cost.
Similarly, one-way CSAs, large thresholds & MTAs, lower margining frequencies … will
give rise to funding costs / benefits.
11. Agenda
1. INTRODUCTION : FVA AND COLLATERALISATION
2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION
3. FUNDING SPREADS VOLATILITY
4. COLLATERALISATION REGIMES & INITIAL MARGINS
12. Copyright © 2014 Murex S.A.S. All rights reserved12
ISDA Margin Survey 2014 [17]
This year, 66% of participants indicated they were referencing terms contained
within their underlying CSAs when pricing derivatives transactions for
collateral margining (CSA discounting).
Also:
91% of all OTC derivatives trades (cleared and non-cleared) were subject to a collateral agreements at the end
of 2013.
90% of non-cleared OTC derivatives trades were subject to collateral agreements at the end of 2013.
87% of non-cleared OTC derivatives collateral agreements relate to portfolios of less than 100 trades.
13. Copyright © 2014 Murex S.A.S. All rights reserved13
CSA-discounting
Uncollateralised trades are priced by discounting Cash Flows on a curve
representing our cost of fund (usually Libor + spread).
Collateralised trades are priced by discounting Cash Flows on a curve
representing the collateral rate (usually OIS rate of a specified currency).
For instance:
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.
Implicitly assumes that for each 𝑡 there is a single funded amount 𝑉(𝑡) and a
single funding rate 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤 or 𝑆𝑐𝑜𝑙𝑙𝑎𝑡
Transactions are held to maturity and term-funded
14. Copyright © 2014 Murex S.A.S. All rights reserved14
CSA-discounting assumptions
In practice, this hypothesis implies that we postulate:
strong “ideal CSA” assumptions
Bilateral (2-way CSA) with continuous margining
Cash equivalent collateral
0-thresholds, MTAs, Rounding, IAs
No IMs
Full substitution and re-hypothecation rights
and that funding spreads are
symmetrical (lending/borrowing)
fixed (and obviously independent from exposure drivers)
usual consensus that, so far, the “ideal CSA” assumption has worked for the bulk
of interbank portfolios on “classical” CSAs and for uncollateralised positions as
well.
15. Copyright © 2014 Murex S.A.S. All rights reserved15
CSA-discounting in practice
Relatively simple implementation in FO systems:
May lead to maintaining very large number of collateral funding curves (CF currency vs. Collateral
currency vs. Collateral rate) and large curve routing tables
Data management investments required (linking FO pricers with Collateral data)
Multi-curve set-up (joint calibration of multiple curves, etc.)
The devil is in the details
Careful attention is required to properly handle pricing and risk analysis of some corner cases –
often needing additional work (systems configuration or updates to pricing libraries) :
Uncollateralised CMS cap (CMS rate derived from collateralised instruments)
EUR collateralised AUD swaption with delivery settlement (and upfront premium)
Uncollateralised swap with mandatory mutual break (risk free close-out)
Collateral currency switch “option”
Hedging uncollateralised positions with collateralised derivatives:
Hedge ratios need to be adjusted
Basis risk remains with originating desk
16. Copyright © 2014 Murex S.A.S. All rights reserved16
FVA via Exposure Simulation
Another approach consists in extending the existing CVA simulation
framework:
All trades are discounted on their relevant “risk-free” OIS benchmark for pricing,
regardless of the collateral agreement details
Exposures and Collateral balances are simulated explicitly taking into account the full
details of the collateral agreement (coverage, thresholds, collateral currency, haircuts, IMs,
etc.)
FVA is measured by taking the integral of discounted exposures/liabilities weighted by the
appropriate funding spreads (if desired, different rates can be applied for the lending &
borrowing cases).
17. Copyright © 2014 Murex S.A.S. All rights reserved17
FVA via Exposure Simulation
Funding spreads are measured between the effective Collateral rate and the chosen
reference risk-free funding rate
Similar to the CSA discounting case, with the option of also evolving spreads as a stochastic risk
factor
Behavioural assumptions can be made regarding the :
Counterparty's choice of collateral assets (currency switch option, cash/securities mix).
Assumed funding lifetime of the positions
Effective rehypothecation ratio / repo haircuts of illiquid securities (RMBS, corporate / municipal
bonds, etc.) and counterparty’s own bonds on stressed scenarios.
FVA can be simply split into sub-components:
FBA vs. FVA
FVA, LVA, CollVA, MVA… (e.g. separating CDS-Bond basis liquidity spread from the credit spread, or
isolating the funding component due to collateral excesses/shortfalls).
P&L attribution elements
18. Copyright © 2014 Murex S.A.S. All rights reserved18
Exposure simulation : FVA vs. CVA/DVA
One may choose to apply different funding curves to Exposures and Liabilities
(akin to CVA & DVA), or take a view that theTrading desk is structurally net
short/long funding and that the funding unit /Treasury will charge an average
rate.
From a funding perspective Cash Flows always net, regardless of Close-Out
netting agreements
Funding costs/benefits occur as long as the institution operates as a going concern:
Some Wrong Way Risk adjustments may thus differ between DVA and FVA (JTD scenarios,
Recovery correlated with exposure factors).
First intuition is that Exposures should be weighted by the survival probabilities of both parties
when computing FVA (similar to first-to-default CVA)
Nevertheless this can be disputed as different results can be derived depending on business assumptions
(risk-free vs. risky close-out, set-off strategies, credit-contingent pay-offs and CSAs…)
Usually a minor effect.
Credit-focused “Margin Period of Risk” assumptions should not be applied to FVA, only the re-
margining frequency should be considered since interests are computed from the value date of
the margin call.
19. Copyright © 2014 Murex S.A.S. All rights reserved19
Exposure simulation : FVA vs. CVA/DVA
Simulation
dateTi
Collateral Balance (CVA/DVA)
Margin Period of Risk (e.g. 10d)
Ti - MPR
margining
frequency
Ti - MF
Collateral
Balance (FVA)
Collateral
Funding
close-out
grace
period
dispute fail
margining
frequency
Credit-focused “Margin Period of Risk” assumptions should not be applied to FVA.
20. Copyright © 2014 Murex S.A.S. All rights reserved20
Imperfect Collateralisation modelling challenges
CSA-Discounting vs. FVA via exposure simulation
21. Copyright © 2014 Murex S.A.S. All rights reserved21
Imperfect Collateralisation modelling challenges
The question is whether a CSA discounting approach alone can be used to price
incrementally without the risk of providing distorted incentives:
Depends on the portfolio in place (transactions and agreements) and magnitude of the impacts.
E.g. if clearing of a given product can happen only on a single CCP.
Option to fix some of the CSA-discounting shortfalls by fiddling with the pricing and curve
libraries.
Strong intuition that aggregation-dependent effects (VaR-based IMs, one-way CSAs) should be
modeled upfront
Whether the volatility of spreads and their correlation with exposure factors can have a material
impact is less clear (apart from obvious pathological cases)
22. Agenda
1. INTRODUCTION : FVA AND COLLATERALISATION
2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION
3. FUNDING SPREADS VOLATILITY
4. COLLATERALISATION REGIMES & INITIAL MARGINS
23. Copyright © 2014 Murex S.A.S. All rights reserved23
Funding spread decisions
Which funding curve?
Own CDS – liquidity basis
OIS-LIBOR + spread
Blended curves
Different curves for legal entities
Symmetric funding curve ?
Different choices depending on the valuation context:
FairValue accounting : what is a reasonable proxy for the average market funding spread?
Is “own funding cost” a justifiable option?
CDX/Itraxx Financials ; LIBOR + spread …
EconomicValue : own cost of funds, as charged by FVA desk / Treasury
24. Copyright © 2014 Murex S.A.S. All rights reserved24
One possible FVA operational model
All trades are priced with OIS discounting and FVA adjustment:
Funding costs are priced via FVA adjustment(s), like credit is priced via CVA
FVA fees and positions are transferred to a FVA desk (can be part of Treasury or CVA desk),
leaving limited IR basis risks in the trading portfolio. Hedge ratios are identical for collateralised /
uncollateralised positions in the trader’s book.
A dedicated desk, reports and manages the Funding P&L (analysis, hedging / reserving for basis
effects, etc.)
As a default rule, assume that all trades are held to maturity (i.e. full lifetime
term-funding)
Some exceptions can be granted for specific counterparties (hedge funds) in order to price
competitively, they are managed through ad hoc processes.
Transaction extensions / roll-overs (or cash settled swaptions, exercised in delivery mode) incur
an incremental FVA charge – consistent with CVA.
Conversely early-terminations/unwinds can get back a FVA benefit fee.
25. Copyright © 2014 Murex S.A.S. All rights reserved25
One possible FVA operational model
Regarding the funding curve, an arrangement can be made with the FVA/Treasury desk:
Treasury agrees to apply a single FTP/funding rate (lend & borrow) based for a year on an industry
benchmark (e.g. Libor + Xbp) - cf. Smirnov [9]
This rate is guaranteed for as long as the trading desk maintains positions within pre-agreed limits (gaps,
CF ladders, PV01s…). Otherwise punitive rates are applied.
A reserve is passed at the BU level to cover for the risk of higher reset of the funding at year end (period
cost)
Additional costs
Contribution to Liquidity buffer is not included in transaction prices as Treasury/ALM takes the
responsibility to optimize the funding strategy (this premium is already included in the internal funding
rate)
LCR/NSFR contributions can be incorporated in a KVA adjustment
The CVA/FVA desk,Treasury and the Collateral Management function need to
collaborate closely
Continuous alignment of pricing assumptions with Collateral Management practices (substitutions,re-
hypothecation…)
Securities assets optimization (collateral & regulator capital)
Data management, implementation of new CSAs…
26. Copyright © 2014 Murex S.A.S. All rights reserved26
Historical analysis : LIBOR-OIS spreads
0
20
40
60
80
100
120
140
160
180
200
EUR Libor - EONIA spread (in bps)
Spread
0
20
40
60
80
100
120
140
160
180
200
EURIBOR - EONIA Spread
Itraxx Senior Financial (Normalised)
EUR EONIA spreads Vs Credit spreads
0
50
100
150
200
250
300
350
400
450
500 USD Libor - FF spread (in bps)
Spread
0
50
100
150
200
250
300
350
400
450
500
USD Libor - FF spread
CDX Financial 5Y (Normalised)
USD Libor - FF spread (in bps)
27. Copyright © 2014 Murex S.A.S. All rights reserved27
0
50
100
150
200
250
300
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
195
205
215
225
235
255
270
280
290
300
310
325
345
390
420
450
Historical spread distribution 2007-2014
Numberofoccurences
Spread level
0
50
100
150
200
250
300
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 80
Historical spread distribution 2010-2014
LIBOR-OIS spreads distributions
28. Copyright © 2014 Murex S.A.S. All rights reserved28
From August 2007, clear de-correlation patterns are observed between EONIA and
EURIBOR 6M swap rates.
De-correlation is stronger on longer maturities.
Correlation levels dropped down to 75% on the 10 years maturity.
Following graphs show 6M sliding historical log-return correlations, for 2y and 10y maturities.
Subprimes crisis
Lehman Brothers
Greek crisis
Historical analysis : LIBOR vs. OIS swap rates
29. Copyright © 2014 Murex S.A.S. All rights reserved29
Stochastic basis spreads experiment
Use a simple short rate model (Hull & White 1 factor) to evolve jointly the forward
estimation and discount curves as correlated processes
Discount curve short rate rt: ∀𝑡 ≥ 0, 𝑟𝑡 = 𝑓 0, 𝑡 + 𝑥𝑡 + 𝜑 𝑡 ; 𝑑𝑥𝑡 = −𝑎𝑥𝑡 𝑑𝑡 + 𝜎 𝑡 𝑑𝑊𝑡 𝑥
; 𝑥0 = 0
Estimation curve short rate st: ∀𝑡 ≥ 0, 𝑠𝑡 = 𝑔 0, 𝑡 + 𝑦𝑡 + 𝜓 𝑡 ; 𝑑𝑦𝑡 = −𝑏𝑦𝑡 𝑑𝑡 + 𝜂 𝑡 𝑑𝑊𝑡 𝑦
; 𝑦0 = 0
where :
• 𝒇 𝟎, 𝒕 (resp. 𝒈 𝟎, 𝒕 ) is the forward short rate at time 0 for date t observed in the market for the discount curve (resp. estimation
curve)
• a and b are two mean reversion rates, 𝝈 𝒕 and 𝜼 𝒕 are two piecewise constant volatility functions
• (𝑾𝒕 𝒙
) and (𝑾𝒕 𝒚
) are two correlated standard Brownian motions, with a constant instantaneous correlation: d 𝑾𝒕
𝒙
, 𝑾𝒕
𝒚
= 𝝆𝒅𝒕
• 𝝋 𝒕 and 𝝍 𝒕 are two deterministic shifts
Assess the impact on the FVA of a simple payer swap:
3Y, Pay fix 0.5%, Receive Euribor 6M
CSA Discounting & Exposure simulation FVA match exactly with correlation at 1 (i.e. deterministic spreads)
30. Copyright © 2014 Murex S.A.S. All rights reserved30
Stochastic basis spreads experiment
FVA increases as correlation decreases (spread volatilities increases)
Realised spread distributions at 3Y for different correlation values
Obviously not the ideal model for OIS/LIBOR spreads with significant de-correlation.
0,2
0,3
0,4
0,5
0,6
0,7
0,68 0,78 0,88 0,98
EURIBOR / EONIA correlation
FVA in Bps
0
200
400
600
800
1000
0 5 10 15 20 25 30 35 40 45 50 55 60
0
20
40
60
80
100
-425
-315
-265
-215
-165
-115
-65
-15
35
85
135
185
235
285
335
400
0
20
40
60
80
-525
-370
-310
-250
-190
-130
-70
-10
50
110
170
230
290
350
410
470
0.95 0.8 0.7
31. Copyright © 2014 Murex S.A.S. All rights reserved31
Spreads vs. exposure factors co-dependence (WWR)
Intuition that Credit Risk represent a significant portion of Funding Spreads
(cf. historical analysis)
Funding costs can be “correlated” with factor(s) driving as well the Funded
Amount (e.g. interest rates, credit spreads or FX levels)
Use a portfolio WWR risk model like Hull & White 2011 [7]
Express default intensities / spreads as a parametric function of an underlying observable variable
(e.g. FX or ZC rate, MV of the bank trading portfolio, but also a stochastic OIS-LIBOR spread
factor or a function of observables…)
Hull & White propose two functional forms :
32. Copyright © 2014 Murex S.A.S. All rights reserved32
Form Std deviation 3bp Std deviation 15bp Std deviation 25bp
1
2
Increasing B
Spreads vs. exposure factors co-dependence (WWR)
Example
Calibrate a(t) to match LIBOR spread
expectations (from rate curve)
B is computed to match historical
standard deviation (e.g. OIS-LIBOR : 12bp for 2010-14, 55 for 2007-14)
33. Copyright © 2014 Murex S.A.S. All rights reserved33
FX & Cross Currency swap RWR example
e.g. expect a funding costs increase if EUR depreciates
4Y, Pay EUR EONIA 6M, Receive USD LIBOR 6M
Funding spread = OIS-Libor + 40bp
X set as FX, MV or EE pathwise
FVA switches from a benefit to a cost.
34. Copyright © 2014 Murex S.A.S. All rights reserved34
Real-life examples
SSAs hedging bonds issuances:
Long-Term IRD positions with One-way CSAs
Alternatively the Counterparty posts their Own Bond as Collateral : no reduction of CVA.
Recover funding benefit in normal market conditions, but funding benefit may vanish in stressed
market (inability to repo large positions, rising haircuts…)
Selling structured products hedges to Corporates
Local bank selling structure back-to-back : uncollateralised with corporate, collateralised with hedge
counterparty (e.g.TARFS,TARNS,Accumulators, PRDCs…)
Hedging products, hence often believed to carry no CVA WWR, or even be Right Way positions
Often packaged as 0-premium notes:
Attractive rate for customer (e.g; carry trade, ITM options),but with limited upside (target redemption or KO)
Reverse position for the bank knocking in at OTM level, often with gearing
Competitive markets (very popular products can turn into crowded trades)
Very asymmetric pay-offs : potential for high funding requirements, and specific WWR (gearing and
one-way market)
Local banks funding spreads can be strongly correlated to large moves in the underlying asset price
35. Copyright © 2014 Murex S.A.S. All rights reserved35
CNYTarget Redemption Forward example
CNY/USD rate – Source: Bloomberg
Hugely popular structure in Asia
Anticipated constant appreciation of the CNY
Typically monthly strips of FX options (vanillas and KI
barriers), with redemption clause and gearing.
Feb 18, PBoC starts fixing the USD/CNY higher and doubles
the authorised daily variation range
36. Copyright © 2014 Murex S.A.S. All rights reserved36
CNYTarget Redemption Forward example
Average KI strikes in the market for outstanding transactions in the 6.15 – 6.20 range.
Morgan Stanley estimates USD 150bn of outstanding notional.
Estimate that above 6.2 corporates will lose USD 200m a month per 0.1 move (contracts are 24months…)
Taiwanese banks in the spotlight after they asked their corporates to post collateral
FSC taking actions against four banks
In parallel skyrocketing funding costs forTaiwanese banks (collateralised in USD),TAIFX (interbank
USD/TWD funding) has risen to 1.53% in April from ~0.85% from Jun to Nov 2013.
In summary, for the issuing bank :
- CVA: General RWR + Specific
WRW
- FVA : WWR
A taste of déjà vu (cf. 2008 Korea,
Brazil, Indonesia, Poland…)
cf. R. Dodd [2] and [10b]
37. Copyright © 2014 Murex S.A.S. All rights reserved37
TARF/KIKOToy Example
Payoff function (from the BANK perspective):
FX Tarf USD/THB: Maturity 2y, N=1M USD,
Monthly payment. Forward 2y at 36 (Spot 35.29)
Funding at 20bp (fix) over interbank
funding spread (variable)
Ignoring all WRW effects:
USD/THB
0
33 36,4 41
Payoff
Gearing Factor 2.0
Monthly TARF payoff function
PFE, PFL & MTM EE, EL & MTM
38. Copyright © 2014 Murex S.A.S. All rights reserved38
TARF/KIKOToy Example
Funding at 20bp (fix) over interbank funding spread (variable)
WWR on FX spot, the following B values generate the following distributions for the
interbank funding spread portion:
39. Copyright © 2014 Murex S.A.S. All rights reserved39
TARF/KIKOToy Example
Taking the funding B(FX) as 0.1, we get a 65% increase in FVA
Adding similar dynamics for CVA :
General RWR on FX (the corporate is hedging against THB appreciation)
Specific WWR on the structure’s MtM (due to gearing, default probabilities rise sharply
once the MtM rises beyond certain levels)
We get the following results with a 78% XVA increase due to combinedWWR
effects on funding costs and credit risk.
40. Copyright © 2014 Murex S.A.S. All rights reserved40
TARF/KIKOToy Example
Counterparty’s credit spreads distributions at 2Y points for varying B(FX) and B(MtM):
41. Copyright © 2014 Murex S.A.S. All rights reserved41
TARF/KIKOToy Example
0
100
200
300
400
500
600
0,02 0,05 0,1 0,3
FVAVariation in % as a function of b(FX)
-200
-150
-100
-50
0
50
100
150
200
250
300
1 2 3
CVA WWR MV
CVA RWR FX
CVA variation in % (for increasing b values)
RWR
WWR
CVA
Specific WWR
General RWR
42. Agenda
1. INTRODUCTION : FVA AND COLLATERALISATION
2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION
3. FUNDING SPREADS VOLATILITY
4. COLLATERALISATION REGIMES & INITIAL MARGINS
43. Copyright © 2014 Murex S.A.S. All rights reserved43
Centrally Cleared Portfolios
Practically no CVA (quasi default-free entity) and no DVA (the CCP is over-
collateralized).
Collateral balance is split inVM & IM:
VM:Variation Margin (covers current MtM)
IM: Initial Margin (covers the collateral gap risk over the liquidation period, e.g. 5 open days)
Multipliers : Credit, Liquidity, Concentration…
CCP pays back an OIS rate minus a spread on Cash Collateral received, not
necessarily on Securities.
44. Copyright © 2014 Murex S.A.S. All rights reserved44
Centrally Cleared Portfolios
On-going clearing costs for DCMs:
Unsecured funding of excess collateral balance :
Function of the trade specifics w.r.t the legacy portfolio and the CCP methodology, as well as
effective collateral rate
Proposal : should be handled as a trade-level variable cost and measured a priori.
Default fund contribution :
Monthly charge function of the relative volume transacted with the CCP vs. other participants.
Can only be measured a posteriori
Proposal : handled as a business unit level period cost (that can be reserved for) since the impact
of a single trade is unclear and this component should not drive the decision to make an
incremental transaction.
Other Costs:
Clearing Fees (semi-variable: fixed+volume based), Settlement & CSD charges, Bank Charges,
Operating costs
Can be allocated as trade variable costs, can be difficult to analyse but require no complex
modelling
45. Copyright © 2014 Murex S.A.S. All rights reserved45
Centrally Cleared Portfolios
Proposed setup for Economic value FVA :
Model cost of funding IMs as part of FVA adjustment at trade-level
Allocate Default Funds & Liquidity Buffer costs as BUs fixed costs
(monthly reserves and profitability targets)
Incorporate other trade-volume based operational expenses as variable costs,
if deemed sufficiently material
46. Copyright © 2014 Murex S.A.S. All rights reserved46
Centrally Cleared Portfolios : computation of IMs
Different CCPs can apply different methodogies
Listed products usually SPAN-based methods
OTC derivatives usuallyVaR-based:
10 years historical series with EWMA decay (e.g. LCH SwapClear) or EWMA vol re-
scaling
(cf. Hull &White [6]).
5d/10d risk factor shocks are applied (with overlapping sampling)
High percentileVaR or Expected Shortfall (e.g. 99.7%)
CCP-specific pricing conventions (e.g. OIS discounting)
Credit & Liquidity Multipliers:
Can be material too
Can show some cliff effects
47. Copyright © 2014 Murex S.A.S. All rights reserved47
The new CSAs
New regulation aiming at “reducing systemic risk and promoting central clearing”
BCBS-IOSCO “Margin requirements for non-centrally cleared derivatives”, bcbs 261, Sep 2013 [14]
ESMA-EBA “Draft RTS on risk-mitigation techniques for OTC-derivative contracts not cleared by a
CCP”, Apr 2014 , on-going consultation [15]
Applicable to Financial Institutions (interbank) with over €8bn notional of non-centrally cleared
derivatives - gradual roll-out from Dec 2015 to Dec 2019
Key provisions in a FVA context
Mandatory exchange of “two-way initial margins”
Margin segregations and no re-hypothecation / re-use rights
Internal models or Standardised schedule methods for determining IMs and collateral haircuts
FX mismatch haircut
Group-level threshold (max €50m) across legal entities and netting agreements
De facto killed the S-CSA initiative
Dec 2013 : ISDA SIMM proposal for an internal model Initial [16]
Expected May 2014 : proposals for an S-SCSA II
48. Copyright © 2014 Murex S.A.S. All rights reserved48
New CSA : zoom on IM requirements
FX cash products exempted, as well as final Notional exchange in CCS
Standardised IM schedule
Very simple to implement, ideal for dispute resolution
Too conservative for most firms (40/60 NGR rule)
BCBS footnote 17 [14] : can we hope to see a move to the more sensible SA-CCR method (with
a rescaling of the Margin add-on to 99% PFE)?
Internal Models
Complex, require regulatory approval
Firm-specific models are impossible to manage for disputes
Need to converge to market standard (e.g. ISDA SIMM, or 3rd party provider)
Consistent with 99% PFE (1%VaR)
Calibration period of at least 3Y and with at least 25% of stressed data
Minimum liquidity horizon of 10d
Positions split in 4 asset classes : (1) IRD, FX & Gold, (2) Equities, (3) Credit, (4) Commodities &
Others. No offsets allowed across asset classes.
49. Copyright © 2014 Murex S.A.S. All rights reserved49
Should IMs be considered in trade-level FVAs?
Conceptually, valuing the incremental IMs funding impact is meaningful when
pricing new operations:
A variable cost relevant at the trade level (e.g. will the trade hedge or diversify the existing
Margining Node portfolio?)
Directly linked to practical business decisions such as the choice of CCP / Counterparty for
execution (function of IM methodology and legacy portfolio)
However, are IMs material enough ?
Obviously extremely variable and a function of the leverage and directionality of the portfolio
being cleared/collateralised
Simplistic example :
Assume a portfolio’s value is normally distributed (IID)
Compare the daily IMs with the portfolio average MtM, depending on the average “age” of the positions
IM replication benchmark runs (IRD portfolios)
50. Copyright © 2014 Murex S.A.S. All rights reserved50
Should IMs be considered in trade-level FVAs?
Are IMs material enough ?
Simplistic example : Margin replication benchmark exercise
on IRD portfolios:
51. Copyright © 2014 Murex S.A.S. All rights reserved51
ModellingVaR-based IMs for FVA
52. Copyright © 2014 Murex S.A.S. All rights reserved52
VM balance
IM+ (e.g.VaR 1%)
IM- (e.g.VaR 99%)
ModellingVaR-based IMs for FVA
Liquidation horizon
53. Copyright © 2014 Murex S.A.S. All rights reserved53
ModellingVaR-based IMs for FVA
VM balance
Collateral posted by Counterparty
Collateral posted by us
54. Copyright © 2014 Murex S.A.S. All rights reserved54
Measuring IMs contributions to FVA
Main question : is the co-dependence between spread and IM exposure drivers a
second order effect that can be neglected?
Various methods are being implemented, for instance:
Crude approximation #1: forwardVaR contributions
Typically when the institution does not have a full-fledged incremental CVA/FVA pricing
framework
Run HsVaR IM calculation on the Margining Node portfolio
Ignores as well asymmetry in volatility profiles over future time-points , path-dependent effects
(e.g. delivery settled swaptions, exotics…), VM-IM funding offset option…
Usually incorrect ageing of portfolio (usuallyVaR systems do not “age” the deals), implicitly
assuming a “constant-state” portfolio except for maturing deals which are dropped
Consider then pricing all trades with OIS discounting and charge all FVA costs a posteriori only?
55. Copyright © 2014 Murex S.A.S. All rights reserved55
Measuring IMs contributions to FVA
Crude approximation #2: within the CVA/FVA exposure simulation
At each future time point sample the distribution of Margin Node portfolio value
Extract the required local VaR / volatility estimate, scale it to the required liquidity horizon and
apply required multipliers
Apply the collateral balance functions as per the normal case (cash/securities mix, appropriate
funding spreads) to derive FVA / MVA
Ignores as well asymmetry in forward volatility profiles, assumes independence of spreads with
exposure factors, etc.
56. Copyright © 2014 Murex S.A.S. All rights reserved56
Measuring IMs contributions to FVA
More accurate approaches typically leverage an existing CVA simulation framework
(or AMC for exotics pricing).
Option 1 : Taylor-VaR
Output first-order sensitivities by scenario path and time step (possibly using a reduced set of scenarios).
AAD or sensitivities approximated by regression are possible options
ApplyVaR scenario and revalue the portfolio via aTaylor-Expansion – Note that this corresponds to the proposed
ISDA SIMM approach.
Option 2 : LSMC regression
View each Margin Node portfolio as an exotic trade pay-off
Oversample the initial Monte Carlo draw to have enough observations for extreme quantiles (e.g. 99%VaR on the
99% PFE scenario point). Efficient implementation with GPUs.
Select a limited number of basis functions relevant to the portfolio (e.g. pre-defined for clearing pools or estimate
sensitivities on forward path central scenario…), then regress the portfolio’s “continuation value” against the basis
functions in backward induction pass.
Apply theVaR scenarios on the resulting portfolio pricing function. Forward pass can use only a subset of the initial
scenarios.
Option 3 : Resampling of AMC simulation values
Based on chosen observables work-out transition probability kernel from scenario i at point t, to all scenarios j at
date t+1
Approximate HistVaR by local conditional distribution function (MC on MC)
57. Copyright © 2014 Murex S.A.S. All rights reserved57
Local regression for LSMC-based IM simulation
In low dimensions (e.g. clearing), local regression methods (LOWESS) can be an
interesting alternative to the usual parametric forms (e.g. polynomials).
Significant accuracy improvement on high “PFE” quantiles for exotic pay-offs
LSMC PFE accuracy w.r.t closed-form pricing (cf. Morali [12])
Parametric
regression
Local
regression
58. Copyright © 2014 Murex S.A.S. All rights reserved58
FVA vs.VaR methodology questions
IM Calculations :
Historical Simulation
Calibration to historical series since wantVaR to use
Real-World probability measure
Assume no drift, no mean-reversion
Regulatory IMs require the inclusion of a “period of
stress” : another probability measure
FVA exposure simulations:
Monte Carlo Simulation
Implementations usually use Risk Neutral
calibration
Risk factor evolution models (drift, MR, volatilities
term-structure)
Is FVA estimated in the Risk-Neutral or Real World measure?
Approximations will have to be used, esp. for translating VaR scenarios in the forward simulation
Initialization of path-wise calibration time series should be avoided :
Potentially complex (e.g. filtering or vol rescaling)
Undesirable “change of volatility regime” from today onwards, impact of mean-reversion over long-horizons
Can we assume equivalence between:
Historical and Monte CarloVaR?
Risk Neutral – Real World equivalence by a change of measure and use RN calibration for VaR
For regulatory IM, apply a change of measure or a simple volatilities scale-up (Stressed Measure for Real-World Measure)?
Handling ofVaR scenarios on risk factors not captured in the FVA simulation / Margining node pricing function
59. Copyright © 2014 Murex S.A.S. All rights reserved59
Challenges in measuring CVA/FVA
InteDelta / Murex - May 2014 : “CVA & Counterparty Risk Management survey”
Top 4 challenges highlighted [13] :
http://survey.murex.com/content/Intedelta_CVA_and_Counterparty_Risk_Survey
60. Copyright © 2014 Murex S.A.S. All rights reserved60
How did regulation impact collateral funding ?
Dodd Frank / EMIR - Centrally cleared derivatives:
CCPs IMs requirements generate a significant additional funding cost
Effective collateral rate is not OIS (fees, handling of securities assets)
BCBS 261 - New CSA’s impacts on effective collateral funding spread:
Margin Segregation
Re-hypothecation now effectively disallowed
BCBS 261 - New CSA’s impacts on the collateral balance and funded amounts:
FX mismatch haircuts
The group level EUR 50M threshold (somewhat increases complexity : how should allocate
corresponding Collateral shortfalls across entities & netting sets).
Regulatory haircuts (Schedule or IMM) calibrated for systemic shocks
Two-way posting of Initial Margins
61. Copyright © 2014 Murex S.A.S. All rights reserved61
Conclusion
Computing FVA for EconomicValue assessment or FairValue Accounting
purpose may warrant using different modelling approaches, both in terms of
methodology and inputs (e.g. choice of funding curves)
In the near future, the bulk of OTC derivatives positions will be split across:
Centrally cleared position (largest portion), where IMs, multipliers and default fund contributions
generate additional funding requirements
New style CSAs (with two-ways IMs, re-hypothecation and haircuts)
Some old-style CSAs with buy-side institutions, corporates & SSAs – sometimes with the usual
twists (one-way, thresholds…)
Exotics and uncollateralised transactions with corporates, SSAs (often structured trns), that can
be quite sensitive to stochastic funding spreads and WWR effects.
In order to price incremental operations in a way that recognizes the economic
benefits/costs of funding, a plain CSA discounting valuation approach will not
suffice anymore.
It may even provide distorted incentives by missing some important effects.
Current CSA discounting implementations, will need to be complemented by additional
computations (e.g. MVA) or replaced by comprehensive exposure simulations.
62. Copyright © 2014 Murex S.A.S. All rights reserved62
Acknowledgments
Sincere thanks to Murex colleagues, and in particular:
Guillaume Juge
Thibault Phlipponneau
AdrienTaÿ-Pamart
63. Copyright © 2014 Murex S.A.S. All rights reserved63
References
Industry papers
[1] G. Cesari & a. - 2009
« Modelling, Pricing, and Hedging Counterparty Credit Exposure.ATechnical Guide »
[2] R. Dodd, IMF paper – July 2009
« Exotic Derivatives Losses in Emerging Markets: Questions of Suitability, Concerns for Stability »
[3]C. Fries – February 2011
« Funded replication:Valuing with stochastic funding »
[4] A. Green, C. Kenyon,and C. R. Dennis – February 2014
« KVA: CapitalValuation Adjustment »
[5] J. Gregory – 2009
« Counterparty credit risk –The new challenge for global financial markets. »
[6] J. Hull & A.White – March 1998
« Incorporating volatility updating into the historical simulation for value at risk »
[7] J. Hull & A.White – June 2011
« CVA & WrongWay Risk »
[8] M. Morini,WBS Fixed income conference – October 2012
« Model risk in today’s approaches to funding and collateral »
[9] I. Smirnov,WBS Fixed income conference – October 2013
« Liquidity & Capital in derivatives pricing »
64. Copyright © 2014 Murex S.A.S. All rights reserved64
References
Murex documents
[10] A. Bon,WBS CVA conference – March 2012
« OTC Collateralisation : Implementation Issues in CVA & FVA frameworks »
[10b] A. Bon – September 2010
« Specific WWR examples – case 3 : from right way to wrong way »
[11] D. Loiseau, MathFinance conference, March 2012
« Introducing Stochastic Spreads in a Multi-Curves Framework »
[12] A. Morali, HPCFinance Conference – May 2013
« American Monte Carlo for Portfolio CVA & PFE »
[13] InteDelta & Murex – May 2014
« CVA & Counterparty Risk Management : a survey of management, measurement and systems »
http://survey.murex.com/content/Intedelta_CVA_and_Counterparty_Risk_Survey
Regulation & institutional documents
[14] BCBS-IOSCO – September 2013
« Margin requirements for non-centrally cleared derivatives »
[15] ESMA-EBA – April 2014
« Draft RTS on risk-mitigation techniques for OTC-derivative contracts not cleared by a CCP »
[16] ISDA – December 2013
« Standard Initial Margin Model for Non-Cleared Derivatives »
[17] ISDA – April 2014
« Margin Survey 2014 »