cvafva challenge
DESCRIPTION
A presentation about CVA and FVA at risk conference by a leading expertTRANSCRIPT
Sep 25, 2013
Information Security Identification: Confidential
Practical CVA/FVA Calculations: Complexity and Challenges
Presented by Dongsheng Lu, Managing Director
Sep 25, 2013
Consistent Accounting
Terms Explanation
Fair Valuation of financial Instrument
FVACVAVV FCFair
FairV
Information Security Identification: Confidential
Valuation under fully-collateral assumption
Credit Value Adjustment
One way CVA
Funding Value Adjustment
Funding cost and benefits
Fair
FCV
CVA
FVA
Credit and Funding Concepts
CVA/FVA: both coming from borrowing/lending. Default vs funding. Base: Perfect credit, fully collateralized cash CVA: credit default only FVA: anything related to funding, value of collateral, cost of posting collateral,
Bond spread vs CDS: funded vs non-funded default spread
u’: cpty default risk
Information Security Identification: Confidential
LX=u+L
u’: cpty default risk
u
u’
L
Funding: Balance sheet and Borrowing
Businesses
Capital
Debt Issues
Equity Financial institutions rely heavily on
borrowing and are highly leveraged. The better capitalized, the higher the credit
rating.
Firm’s funding level represents market/investor’s view on firm’s credit as well as market liquidity
Information Security Identification: Confidential
and
Investments
Securities
Asset Liability
as market liquidity
Firm’s Funding activities:
Deposits Issue debt Issue equity Convertible bond Funding centers Practical difficulty to compare different
funding activities
Funding
DeskCpty
Lend $1
LOBMarket
Lender
Lend $1 Lend $1
LOB Lending
LOB Borrowing
CPTY Borrowing
FundDeskBorrowing
FundDeskLending
Market Lending
Unsecured Lending/Borrowing
Information Security Identification: Confidential
-$1
$1.2
$1
-$1.1
$1
-$1.2
$1
-$1.1
-$1
$1.1
-$1
$1.1
t=0
t=T
Internal Funding Transfer
Derivative Activity (CVA/DVA/FVA)
External Borrowing
Assumptions
Applies to financial institutions with high leverage
At any given time, there is an equilibrium funding cost for the firm. Assuming the existence of a funding curve.
Funding policy and operations varies from firm to firm
Given a policy and funding curve
Information Security Identification: Confidential
Firm should be marking the future cash flow exactly the same way, whether it is issued debt or swaps or complex derivatives
Debt issuance spread would give the funding level across maturities
Funding spread include: Firm’s credit, Market’s liquidity
The same discounting should be applied for derivatives
Assumptions
There is one true economic value for each market participant for a given trade
Every market participant’s economic value could be different for the same trade
Different valuation reflects the competitiveness of the market participants
“Market Price” Market’s average exit value
Information Security Identification: Confidential
same way as LIBOR as average funding rate
Valued based on average funding rate
Funding value adjustment (FVA) depends on how one treats all other adjustments
A lot of confusion as to what is FVA
It is a relative value
Base: Fully collateralized. Base + Credit + Funding
Funding value adjustment Collateral value Part of discounting spread
FVA Debate: FVA in Fair Valuations?
LOB1
LOB2
LOB3
Borrow(-)/Lend(+)
+ + +
+ +
+
* *
Total Funding Requirement: Sum of funding cost/benefit
IndividualBusinesses
Information Security Identification: Confidential
Given funding spread X at firm level, all LOBs mark book based on X The sum of funding/cost reflect the total funding requirements at the firm level Funding from outside at firm level balanced with sum of all LOBs funding needs Individual business level funding X marking Equivalent Market value for LOBs +
apply funding X at the firm level Proper incentive for the individual businesses
- - -LOBn
**
**
FVA Debate: FVA in Fair Valuations?
Aggregated Short/Medium/Long term funding needs
Ideally matched funding needs and actual outside funding
Reality Short/Medium term funding liability/borrowing Longer term asset/lending
Information Security Identification: Confidential
Regulations more balanced asset/liability matching in terms
Funding cost should be charged at the individual LOB level to reflect the proper incentive.
Market change: for example, S&P 500 index total return (LIBOR+30/40bps from close to LIBOR flat)
Typical Client Quoting with CVA/FVA
CSA / CCP?
LCH Pricing
CME Pricing
LCH /CME ?
Secured Pricing
CVA ~ 0 Collateral asset
Differential Discounting
Pricing
CCP
YES
LCH
CME
Margin rule + Incrementl Risk
Information Security Identification: Confidential
Fully Collateralized?
Collateral asset Collateral CCY
CSA Pricing
CollateralThrshld
Rating Trigger Break Clause …
Collateralized Portion
Un-collateralized Portion
CVA Funding
Cost/Benefit
CSA
YES
NO
SCEN
SCEN
Other Pricing Terms
Market Hedging Cost Credit Hedging Cost Capital/Balance sheet Charge Profit Margin
Differential Discounting
Classify all funding situations, construct funding curves
Collateral Currency Xccy spread curve Optimal xccy funding
Basic Funding Spread Curves
Base discounting: e.g. USD Collateral Different Currency Different Asset Construct Funding spread curve
Differential Discounting
Information Security Identification: Confidential
Collateral Asset Cash/Treasury Agency GSE Corporates Munis
Break Clause
Dynamic Funding Curve Generation
Max(FND1,FND2, … FNDN)
A Typical Example: JPY Swaption Trading
Differentiate Collateral: JPY or USD or CSA, differential discounting
Differentiate Underlying swap: LCH/CCP or CSA
- LCH Swap: central cleared swap- CSA: different assumptions- Complex situation: mixture discounting CSA+LCH
Information Security Identification: Confidential
- Complex situation: mixture discounting CSA+LCH
Forward vs Spot premiums
Physical vs Cash settlement
Customer trading: CVA, FVA, Capital
t=0 Option Swap
CSA Discounting
LCH Swap: OIS Discounting
Example: A CSA governed Swaption settle into LCH Swap
Information Security Identification: Confidential
t=0 Option Expiry
Swap Maturity
Mixture Discounting Example
Before option expiry, economics follow CSA discounting
After option expiry, settle into LCH swap, native OIS discounting
t=0Break Date 1
Deal Maturity
Credit Risk Exposure
No Credit risk
Example: Break/Trigger/Exit Clause/Mutual Put/Replacement
Information Security Identification: Confidential
Mutual Put, Break/Trigger Clause
CVA: No Credit risk after break date, limited tenor risk paid at day one
FVA: Discounting for cashflow after break date is ambiguous
FVA: Average market funding is LIBOR?
Replacement event ?
Scenario Based CVA/FVA Calculation
Scenario Based Pricing
Rating based threshold scenario rating scenario valuation scenario threshold
Trigger/Exit
No Credit risk after trigger Exiting value calc (LIBOR) Replacement cost
Triggered?
V < 0
Collateralized: Max(-V-H,0)
Collateral discounting
Unsecured: -Min(-V,H)
Information Security Identification: Confidential
scenario threshold
Rating Trigger scenario triggered?
Break Clause
Unsecured: Min(V,H’) Credit Exposure: Min(V,H’) CVA: Min(V,H’)*u’*dt Funding cost: Min(V,H’)*X*dt
Collateralized: Max(V-H’,0) No CVA Collateral Discounting
V < 0
V > 0
No DVA Fund Benefit: Min(-V,H)*X*dt
Scenario Based CVA/FVA Calculation
Market Simulations (M)(e.g. 10,000 paths)
CVAFVA
Aggregation
CSA
ExposureExposure
CreditCredit
CreditCredit
FundingFunding
Information Security Identification: Confidential
Credit Simulations (C)(e.g. 100,000 paths)
Capital Requirement:
Counterparty Credit risk (Basel II) CVA VaR based (Basel III) Advanced/Standardized approach
Challenge: Complex CSAs
Rating Migration
Rating Based ThresholdDowngrade eventsReplacement cost
Break/Default Clause
Mutual put Termination event (ATE)Legal/Netting
Collateral Definition
Collateral AssetCollateral CurrencyHair Cut Initial marginsCollateral Damage
Information Security Identification: Confidential
Need scenario based credit
Credit simulation with migration Apply CSA in scenarios
Additional Exit Event
No credit risk after exit Funding cost calculation Exit event vs market liquidity
Collateral Modeling
Collateral choice: static funding curve. Optionality impractical.
Hair cuts/Margins
Challenge: Massive Computations
Market RiskAny market risk within the normal
derivatives pricing/risk management are risks for CVA/FVA, including rates, FX, stock price, volatility/skew and correlations etc .
Pricing,
Credit Risk
Specific Name riskGeneric credit risk
Live TradingLive Pricing/Quoting Incremental CVA/FVA Calc
Information Security Identification: Confidential
Pricing,Risk Management,
Hedging and Perf Measurement
Generic credit riskDowngrade/Default riskHedging strategy
Wrong Way Risk
Specific counterparty WWR WWR hedge
Capital Requirement
CVA VaR BASEL III Capital Standardize vs Advanced methodology
Challenge: Massive Computations
Market RiskPrice Levels, delta/gammaRates/delta buckets, gamma ladderBasis (Libor basis, xccy basis etc) bucketsVega distribution/Skew exposureCorrelation levels
Credit Risk
Specific Name credit bucketsGeneric Index credit buckets, hedge ratio
Each ScenarioMarket, Credit
Simulations, and
Scenarios Generation
Information Security Identification: Confidential
Generic Index credit buckets, hedge ratio Proxy hedges, hedge ratio
Wrong Way Risk
Different Correlation levels Factor based WWR
Regularoty Requirement
Credit sensitivities for CVA VaR Stress testing: market and credit
Simulations, and Aggregations
Sensitivities Buckets
Hedge Ratio etc
Challenge: Massive Computations
Each ScenarioMarket, Credit
Scenarios Generation
Efficient Computing
Efficient CVA/FVA computation design
Adjoint Algorithmic Differentiation
Information Security Identification: Confidential
Distributed Computing
GRID Computing GPU Computing
Market, Credit Simulations, and
Aggregations
Sensitivities Buckets
Hedge Ratio etc
Node Node Node Node Node
Backward Pricing: credit/funded discounting
Credit Discounting: (similarly for funded discounting)
drttur PRee )1(1)(
)/()/(/ unfundriskfreeVfundedriskyVFVACVA
CVA/FVA Calculations
Forward Simulation: collecting defaults and funding cost/benefits
Information Security Identification: Confidential
E(t): Exposure at risk at time tD(t): discountingX(t): funding spread
T
T
d
dttDtXtEFVA
dttDtPRtECVA
0
0
)()()(
)()()1)((
Forward Simulation: collecting defaults and funding cost/benefits
Backward Discounting:
Pros: Easy to incorporate spread impact Can incorporate credit impact on exercise boundary
Cons:
Difficult to net portfolio of deals with same CSA Difficult to apply more complex CSA terms Difficult to calculate wrong way risk, incremental CVA
Forward Simulation:
Pros: Can net portfolio deals across same CSA easily Can deal with very complex CSA terms easily Fast computation of wrong way risk and incremental CVA
Cons: Need to develop a global simulation model and a complex correlation model Approximation: exercise boundary not affected by credit/funding
Forward Simulations Steps
Consistent multicurrency/asset simulations (IR, FX, Equity … )
Along with credit simulations + ratings transition
Valuation of all instruments once market factor exposure
CVA/FVA Calculations
Valuation of all instruments once market factor exposure
Aggregation of market factor exposure with credit/ratings
Application of netting and CSA
Collect default loss and funding cost/benefits
Credit Rating Collateral Threshold
AAA 50M
AA 20M
A 5M
BBB 0M
Credit Rating Event
BBB Termination
Eligible Currencies
USD
EUR
CSA Complexity
Rating dependency of collateral posting Downgrade provisions Collateral asset/currencies Automatic/Discretionary terminations Legal/Netting opinion
Asset Haircut
Cash 100%
Treasury < 2y 101%
Treasury (2y-5y) 103%
Treasury(5y-10y) 105%
Treasury(>10y) 108%
GSE Passthroughs
115%
Corprts/Munis 120%
GBP
CSA Complexity Modeling
Needs to model ratings in the future Market risk simulation and credit
simulations at the same time Correlations could become important
Challenge: CSA Netting with Complex Portfolio
Generic Time Grid
Generic Time Grid
Specific Trade Pricing:
Trade specific Cashflows, Resets, Notifications, Exercise etc Requires a trade specific time grid Different grid for different deals Different grid for different deals
Specifc Time grid For Deal j
Specifc Time grid For Deal k
Methodology 1:
Market factor calculations based on trade specific grid Regression/interpolation of scenario valuations:
V = V(R,t), R: regression variables Use regressed/interpolated values on generic grid/scenarios Exposures Aggregation of market factor exposures with credit/ratings
Methodology 2:Methodology 2:
Direct valuations based on trade specific grid: simulation based (such as BGM) Exposures are obtained for trade specific grid Interpolate market factor exposures from trade specific grids to generic grid
Methodology 1:
Pros: Can use any trading quality pricing model regression
Cons:
Accuracy of regression/interpolation: explanatory variables and power
Methodology 2:Methodology 2:
Pros: Consistency can be built among all market risk factors
Cons: Need to develop a global simulation model Need consistent correlations among risk factors and for all trades.
Random number Mapping
Random number for generic time grid => derive trade specific grid RN Conserve correlation: equivalent random number generation
Black: Generic Time GridOrange: Trade Specific Grid
dt dt’
dz
dz’’
Known dz’
Need
Black: Generic Time GridOrange: Trade Specific Grid
dt dt’
dz
dz’’
Known dz’
Need
Brownian Bridging Random Number
Orange: Trade Specific Griddz’’dz’’NeedNeed
Adding random numbers:
Correlation Conserved:
Credit simulation:
Aggregation vs market valuations Requires correlations among Market and Credit risk factors Use generic time grid CVA = Credit_Aggregation(CSA, Credit Ratings, Market Values) FVA = Funding_Agg(CSA, Credit Ratings, Market Values, Funding Spread)
Challenge: Credit Simulation and Ratings Migration
Generic Time Grid
FVA = Funding_Agg(CSA, Credit Ratings, Market Values, Funding Spread)
Methodology 1:
Simulate credit spreads in scenarios Map credit spreads to ratings credit migrations
Credit Simulation
Methodology 2:
Structural model simulation using ratings transition matrix Risk neutralization of transition matrix Defaults from ratings migration calibrated to market traded CDS
Credit Simulation: Finite Markov Process + Ratings Transition
Rating k
Default
AAA
A
B
AA
C Dynamic simulation
Rating i Rating j
Rating m
Structural asset model Based on a N-rating system. Probability of defaults calibrated step-wise
1...00
............
...
...
~ 22221
11211
n
n
ppp
ppp
p
Credit Simulation: Transition Matrix Propagation
1...00
1...00
............
...
...
1...00
............
...
...
~ 22221
11211
2
1
22221
11211
Tn
TT
Tn
TT
Tn
T
T
n
n
ppp
ppp
P
P
P
ppp
ppp
p
Credit Simulation: Transition Matrix Propagation
n
t = 1 t = T
Credit Default: Jump to default and Transition to Default
AAA AA A BBB DC
Credit Calibration: Generic Stepwise Transition Matrix Calibration
1
1
2
1
1
1
12
11
......
~
i
dn
i
d
i
d
inn
in
in
t
P
P
P
p
p
p
Pi
Risk Neutralizing Markovian Transition Matrix
P(Default) A B C
1 0.31% 1.72% 6.28%
2 0.72% 4.27% 11.80%
5 2.60% 13.00% 25.60%
10 7.00% 30.00% 48.00%10 7.00% 30.00% 48.00%
TMatrix(Annnual) A B C D
A 96.0% 2.50% 1.19% 0.31%
B 0.40% 83.0% 14.87% 1.73%
C 0.41% 1.00% 92.3% 6.29%
D 0.00% 0.00% 0.00% 100%
Credit Simulation: Structural Asset Model and Calibration
1
2
1
1
12
11
......
~i
d
i
d
in
in
t
P
P
p
p
Pi
Exact Calibration to specific name CDS
Specific name calibration after generic TM calibration From generic TM calibration, probability of default not calibrated exactly In this calibration process, default probabilities are adjusted to match CDS
exactly One can assign partial default to scenarios to match default exactly
11
......i
dn
inn Pp
Market Factors
Base ScenarioMarket/Credit
Correlation Stress
Wrong Way Risk: Market/Credit Correlation Stress)
Correlations
Market Factors
Credit Factors
Keeping same market factor exposure
Solving credit factors incrementally
Credit Risk Hedging with Rating Trigger
AAA AA A BBB DC
Credit Rating Collateral Threshold
AAA 50M
AA 20M
A 5M
BBB 0M
Credit Rating Event
BBB Termination
Incremental CVA Calculation for a New Deal
Given exposure V(ijk) for portfolio Calculate single deal exposure U(ijk) Portfolio CVA = Agg(credit, V) New Portfolio CVA’ = Agg(Credit, U+V) Incremental CVA = CVA’-CVA
Incremental CVA Calculations
Incremental CVA = CVA’-CVA Credit aggregation: fast process
Incremental CVA Calculation for a Existing Deal
Given exposure V(ijk) for portfolio Calculate single deal exposure U(ijk) Portfolio CVA = Agg(credit, V) Portfolio without deal CVA’ = Agg(credit,V-U) Incremental CVA = CVA-CVA’