1. Introduction to Numerix

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The xVA prism:

Current challenges and best

practices

6 February 2014

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Agenda

1. Introduction to Numerix

2. Overview of the regulatory landscape & current market trends

3. The new margining regime: Accounting for collateral under an

unified decision measure

4. Valuation Adjustments and replication

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Section I

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Numerix Overview

 Market leader in Advanced analytics for structuring/managing all derivatives and structured products and risk management and compliance

 200+ employees globally

 Integrated in 3rd party solutions (trading, risk and operations platforms)

Some of our clients Strong resource pool

Global coverage, with support across all major languages

Phds 40%

MBA/Msc 30% CFA 20%

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Section II

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The new regulatory framework for counterparty risk

Basel 3

Capital requirement for OTC bilateral exposures and exposures to CCPs (from January 2014)

IFRS 13

Accounting rules for CVA/DVA – since January 2013

All standardized OTC derivatives should be cleared through CCPs OTC derivative contracts should be reported to trade repository

Exemptions: sovereign and corporates (thresholds, hedging) – III/IVQ 2013

Mandatory Clearing for eligible OTC Derivatives – June 2014

Margin requirement for non centrally cleared OTC – from Dec 2015

EMIR

Solvency

2

Solvency incentivizes high quality collateral selection – From January 2016

BCBS/IOSCO

Mandatory initial margin and variation margin for bilateral OTC transactions _{Segregation and limits to rehypotecation of the amount of collateral that}

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• The new regulatory requirements have accelerated the development and re-definement of valuation and risk methodologies at institutions across the globe with a focus on valuation transparency, margin assessment and risk fortification.

Regulatory-Compliance

Margining & Valuation

Model Validation

Total Value Adjusment

Data & systems

Current market trends

• « New » regime based on Initial/Variation Margin and Collateral Posting • Funding inclusion into pricing aka funding monetization

• Collateral Choice in pricing and optionality (CTD) • Multi-Curve Pricing

• Confidence in the appropriateness of the model (local adaptation) • Transparency for model and parameters

• Confidence that the entity has a good understanding of assumptions, risk drivers and results

• Stress Testing

• Understanding Pricing/Risk decomposition : CVA, DVA, FVA, RVA,… • Risk Integration : market+credit+liquidity in a consistent unified

framework

• Term Structure of eg Multi year TVA

• Continued investment in data and systems, increasing

computation speed and embedding within front office tools and P&L

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Longdated “Unclearables”

Source: ISDA Margin Survey 2013

Source: Tabb Group

Growth in value of collateral agreements for non-cleared OTC derivatives

Notional amount outstanding has grown over the last decade. Aggregate counterparty exposure in terms of net MtM value considering close out netting before collateral has decreased from 3,9 to 3,7 billions Usd from 2011 to 2012 (BIS statistics); collateral value reported has increased, suggesting more exposures being

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Collateral Transformation & Trends

• Mostly handled in the back office

• Low necessity of margin calls (high thresholds and min transfer • amounts

•Few derivatives were collateralized

Before 2008

• Lack of transparency in Structured Credit Notes • Double Defaults

tendency

•One rate regime

• Regulatory Haircuts

2008- 2012

• Increased usage of collateral as a way to mitigate risk of counterparty default •Regulation requirements – CCPs –

Margin calls

• Divergence of rates after the crisis and complex CSAs

• Collateral shortage (high demand, rehypothecation)

• Equally important for sell-side and buy-side

• Choice of collateral significantly affects derivative pricing

•Push from traders and front-office – profit is the drive

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Section III

The new margining regime: Accounting for collateral under an unified

decision measure

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Initial & Variation Margins

• The initial margin is supposed to cover quality of collateral, gap risk, wrong way risk. By design the IM needs to cover the closing out of positions (without the loss) to a CCP in a worst case

scenario.

• Initial margin is an “haircut” (overcollaterisation) which is calculated at inception of the trade. The margin can fluctuate during the liftetime of the trade, given market conditions and remaining risk.

• As its colour varies, several methodologies exist, two of them are proposed for cleared and uncleared positions.

– Cleared position :It is calculated as an historical VaR

capturing a cycle (5-10 years) observation, on shifts of underlying market factors.

– Uncleared position : It is calculated as a Potential Future

Exposure (99% quantile) at 10 day horizon over a stressed market period.

• The Variation margin covers the change in the valuation of the relevant positions as with the collateral in a standard CSA.

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Pricing & Ageing

Hybrid Model

Historical VaR (cleared) or PFE (uncleared)

 

Haircut Optionality

MTA Thresholds Collateral Data Initial Margin Variation Margin FVA

CVA , DVA , RVA, CollVA

Collateral Data

Counterparty Risk Platform

CSA-Netting agreements/ Path dependent Collateralized

Historical

VaR 10 day PFE

Risk Mitigation Strategies

IR (S)BK2F EQ Heston FX Heston IR HW1F IR (S)BK1F IR HW2F IR SV-LMM INF JY

(HW) INF JY (BK) EQ BS EQ Dupire EQ Bates EQ LSV FX BS CMDTY Black CDMTY S1F CMDTY GS2F CMDTY Heston HYBRID MODEL -100.00 -50.00 50.00 100.00 150.00 200.00 250.00 300.00

4/1/2012 8/14/201312/27/20145/10/2016 9/22/2017 2/4/2019 6/18/2020 PFE w Collateral PFE w/o Collateral

Overall Framework

EVA / Limits

PnL Variations

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13 Credit Value

Adjustment

Debit Value

Adjustment

Replacement

Value Adjustment

Margining Value

Adjustment

Funding Value

Adjustment

Risk Cocktail :Valuation Adjustments

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The cocktails ingredients

• The final commercial margin include the following ingredients: • CVA (Credit Value Adjustment) :Adjustment to the risk

free value made by one agent to take into account the potential default of a counterparty defaulting first.

• DVA (Debit Value Adjustment): Adjustment to the risk free value made by the agent to take into account the his potential default first than the counterparty. It also incorporates a funding angle, as bank’s default risk increases, the value of liabilities decreases.

• FVA (Funding Value Adjustment)/LVA: Reflects the cost an institution incurs when hedging an uncollateralized trade with an offsetting position on which collateral is required.

• RVA (Replacement Value Adjustment): reflects the “trigger” cost that replaces a credit quality downgrade of the counterparty with another trade from another counterparty.

• MVA (Margin Value Adjustment): reflects the cost associated with Initial and Variation Margins

• Cost of Capital : Valuation Adjustment for Regulatory Capital

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Section IV

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Origins of xVA

• In the modern world:

– existence of multiple rates corresponding to di

ﬀ

erent possibilities to borrow/lend

money

• rate r

x

collateral rate (almost risk-free rate)

• rate r

r

for asset secured borrowing (“repo”)

• rate r

f

for unsecured funding

• Possibility of default and migration

the classical arbitrage-free theory should be modiﬁed

• We should modify the replication/hedge arguments to include multiple rates and

defaults

• Deﬁnition

.

The TVA (Total Valuation Adjustment)

is the di

ﬀ

erence between the true

(modern) price and the base one. The base price is often related with fully

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

Financial instrument replication (hedging) is a unique way to calculate its fair

price or adjustments xVA (CVA, DVA, FVA etc.)



Different replications lead to di

ﬀ

erent adjustments. There is a big variety of the

adjustments (CVA, DVA, FVA, FCA etc.). Thus, it is important to identify them for

given replication techniques to avoid double-counting.



A portfolio replication (bonds) strategy is designed and used in the context of

hedging default risks for both self and counterparty.



Hedge (replication) against di

ﬀ

erent market movements and defaults:

 Credit spread and default of the counterparty and the bank  Funding costs of the counterparty and the bank

 Assets movements

 Collateral rate movements

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

Piterbarg

(2010)



Borrow/lend money via the bank treasury desk with a unique “funding” rate



The bank default is already taken into account by the treasury "integrated"

rate



Burgard-Kjaer

(2013)



Borrow/lend money with external (w.r.t. the bank) parties: different rates to

borrow and lend.



The rates are related with the bank credit spread and expected recovery.



Multiple replication strategies

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Double-counting counterbalancing effects



Banks are required to hold a DVA adjustment for their own credit risk on

uncollateralized trades



Funding spreads are a function of bank credit quality: by implementing FVA you

are effectively subsuming DVA on payables and accounting for funding on

receivables



Knowledge of the replication/hedging strategy:



gives the unique pricing equation and speciﬁes the TVA



permits to identify parts of the adjustments with xVA’s



prevents from the double-counting

• if we calculate the FVA coming from Piterbarg replication, it will be double-counting to take the DVA into account;

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Implementation

1. Simulate the model rates and all payment indexes

2. Build the single-rate pricing model equipped with Least Square Monte Carlo

3. Calculate future values for all instruments in portfolio on this model (can be

done independently ”instrument-by-instrument” using the Algorithmic Exposure

methods (AIM (2011))– important for parallel computation)

4. Aggregate the instrument future prices into the portfolio ones

5. Calculate the xVA from the obtained future values using universal approximation

formula (ABM (2013)) and its scripted version available in Numerix

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Script example

1. Alexandre Antonov; Numerix FVA for General Instruments: Theory and Practice

PRODUCTS

NONDISCOUNTING SpreadIntegral, FVA NONDISCOUNTING CollateralUnits

TEMPORARY dt, RHS, EffectiveRate, EffectiveSpread, Delta TEMPORARY Collateral, Collateral0, V0, RHS0

END PRODUCTS

PAYOFFSCRIPT

IFISACTIVE(MarginCallDates) THEN

Collateral = CollateralUnits * CollateralAssetValue Delta = MAX(V - HighT, 0) - MAX(- V - LowT, 0) - Collateral Delta = WHEN((Delta > 0) AND(Delta < CTPYMTA), 0, Delta) Delta = WHEN((Delta < 0) AND(Delta > - SELFMTA), 0, Delta) Collateral += Delta

CollateralUnits = Collateral / CollateralAssetValue ENDIF

IFISACTIVE(ObservationDates) THEN

// Calculate true collateral amount

Collateral = CollateralUnits * CollateralAssetValue

// Calculate the true RHS (based on true collateral amount)

RHS = Collateral * r_C + (V - Collateral) * r_F

// Regularization procedure for effective rate calculation:

// Calculate regularized price floored/capped to +-Tolerance

// when V close to zero

V0=WHEN(V>=0, MAX(V, Tolerance), MIN(V, - Tolerance))

// Calculate regularized collateral (ignoring margin call dates and MTA)

// and corresponding regularized RHS

Collateral0 = MAX(V0 - HighT, 0) - MAX(- V0 - LowT, 0) RHS0 = Collateral0 * r_C + (V0 - Collateral0) * r_F

// Calculate regularized effective rate protected from division by zero

// The approximation error is small (higher order than our accuracy)

EffectiveRate = RHS0 / V0

EffectiveSpread = EffectiveRate - r_M

dt = ObservationDatesDCF

SpreadIntegral += EffectiveSpread * dt

// Aggregate the FVA

FVA -=(RHS - r_M * V) * exp(- SpreadIntegral) * DF * dt ENDIF

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Section IV

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Conclusions and potential extensions



Funding and Credit are untimely, implicitly linked and their interplay causes

(some) counterbalancing effects:

 The Initial Margin “wave” for both cleared and non cleared instruments imply higher capital

requirements, with higher funding necessity.

 FVA & DVA monetization dynamics, where DVA, generates funding benefits in asymmetric