The xVA prism:

Current challenges and best

practices 6 February 2014

Alexander Antonov, SVP, Head of Quantitative Research

Alexis Hamar, Sales Manager

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

5. Conclusions

Section I

Introduction to Numerix and Numerix Solutions overview

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%

MA 10%

Section II

Overview of the regulatory landscape and current Market trends

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

covers initial margin; universal threshold established. Phase in from dec

2015

• 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

• Reporting and data Intelligence for real time

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

collateralized.

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

Now

Section III

The new margining regime: Accounting for collateral under an unified

decision measure

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.

• There is a notion of risk transformation of counterparty risk into

liquidity/funding risk, operational and legal risks.

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 8/14/2013 12/27/2014 5/10/2016 9/22/2017 2/4/2019 6/18/2020

PFE w Collateral

PFE w/o Collateral

Overall Framework

EVA / Limits

PnL

Variations

Stress Testing Models

13

Credit Value

Adjustment

Debit Value

Adjustment

Replacement

Value Adjustment

Margining Value

Adjustment

Funding Value

Adjustment

Risk Cocktail :Valuation Adjustments

Collateral Value

Adjustment

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

• CollVA: Cost of collateral (embedded options, currencies,..)

CVA Example: Numerix - Datawatch

CVA Example: Numerix - Datawatch

Section IV

Valuation Adjustments and Replication

Origins of xVA

• In the modern world:

– existence of multiple rates corresponding to different possibilities to borrow/lend

money

• rate rx collateral rate (almost risk-free rate)

• rate rr for asset secured borrowing (“repo”)

• rate rf 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 difference between the true

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

collateralized portfolio.

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

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

Different replications lead to different 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 different 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

Introduction and market movements

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

Replications/Hedging

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;

• if we follow Burgard-Kjaer perfect replication using two bonds, the TVA=CVA+DVA, i.e. using

Piterbarg FVA instead of the DVA will lead to errors

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

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

IF ISACTIVE(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

END IF

IF ISACTIVE(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

END IF

END PAYOFFSCRIPT

Section IV

Conclusions

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

situations.

Systems & Technologies exist today for achieving an integrated xVA approach

to derivative front-to-treasury-risk process

Numerix provides a transparent and complete modeling framework on the xVA

including a set of script templates embedded in platforms as well as a detailed

description of replication strategies and associated adjustments (CVA, DVA,

FVA etc.)

References

Alexandre Antonov, Serguei Issakov and Serguei Mechkov (2011)

"Algorithmic Exposure and CVA for Exotic Derivatives", Available at SSRN

Alexandre Antonov, Marco Bianchetti and Ion Mihai (2013)

"FVA for General Instruments: Theory and Practice", Available at SSRN

Christoph Burgard and Mats Kjaer (2013),

"Funding strategies, funding costs", RISK, Dec

Vladimir Piterbarg (2010),

"Funding beyond discounting: collateral agreements and derivatives pricing",

RISK, Feb.