Structured Credit Solutions

Structured Credit Solutions

February 28, 2008

Robert Stamicar, Research - Methodology

Marianela Hoz de Vila, Account Management – Practical Application

Denny Yu, Account Management - Moderator

Measure Risk of Advanced Structured Credit Trading Strategies

www.riskmetrics.com 2Webcast Series

Agenda

Credit indices – CDX & iTraxxCredit Default Swaps – description and pricing framework

Credit Default Indices – description and pricing framework

Spread decomposition – theoretical fair spread plus index basis

Application to risk management

Analyzing synthetic CDO tranches using base correlationsStress tests using base correlationsCorrelation as a risk factorMapping bespoke tranches to standard index tranches


Credit index modelWhat are we trying to achieve?

Pre-credit index approaches

Credit index instrument

CDS

(single-name model)

Index - No idiosyncratic risk

- No single name stresses

- Short histories for new series

S-CDO (0-100%)

(granular model)

Constituent CDS - Have history but index is ignored

- Calibration not handled

Key Risk Factors Comments

Single-name model Index -“Synthetic” series handles short

history

-Systemic risk

Basket model Constituent CDS +

index basis

- Calibration now possible

- Idiosyncratic risk captured

Synthetic historical series


Agenda







Credit Default Swaps (CDS)

CDS - Contract referencing bond(s) issued by a reference entity betweenProtection buyer – pays a periodic premium (spread)

Protection seller – pays a loss amount if the reference entity defaults

Spread conventionsTypically set at outset such that entry MTM is zero (all running premium).

For distressed credit, running premium is fixed, and the buyer pays an upfront amount that varies according to the market.

MaturityFive years the most liquid, but most maturities from one to ten years trade.

Actual maturity is fixed according to quarterly ISDA dates (20th of Mar, Jun, Sep, Dec)

So maturity of “five-year” CDS ranges from 5 to 5.25 years.

Buyer Sellers

Reference

XYZ

1-Recovery

Buyer Sellers

Reference

XYZ

1-Recovery


Pricing of CDS

CDS pricing: deterministic discount factors, hazard rates

Fair spread: the premium that makes the contract MTM zero

S – survival probability (=1-F) RC – recovery claim

f – default density (=d F/d t)


Calibrating to observed prices

Default probabilities are related to piecewise constant hazard rates through

Common practice is to fit hazards to the spread curve for a given reference

entity using successively longer maturity CDS:Δtk are maturities of observed CDS premia

Find h1 to match fair spread at Δt1Given h1… hk, find hk+1 to match fair spread at Δtk+1


Credit default indices (CDX)

Various mergers have produced standard index families: CDX (North

America) and iTraxx (Europe and Asia).

Credit index: Contract references a standard basket of n reference entitiesProtection buyer – pays a fixed running premium on the remaining notional

Protection seller – pays a loss amount when a reference entity defaults

Equally weighted

On a default eventNotional amount is reduced by 1/nProtection seller pays loss on a notional amount of 1/nContract continues on remaining basket until maturity


Credit default index mechanics

Contracts are standardized: on a single contract, all participants tradeSame basket of names

Same maturity date

Same running premium

Every six months (ISDA dates of Mar and Sep), the contract “rolls”New basket defined (5-10% turnover is typical)

New maturity date, new (maybe) running premium

Investors may remain in previous contract (fixed basket), or roll into new on-the-run contract (fixed duration)

Roll schedule implies that maturity of “five-year” index ranges from 4.75 to

5.25 years.

Trade on a price basisRunning premium is fixed

Upfront amount paid by either the buyer or seller to enter the contract.


Pricing of credit index (as a basket)

Credit Index Pricing: n reference credits

Observe…If all the default probabilities are equal, this reduces to the single name case.

This is not a correlation product! Only marginal default distributions enter.

Can define the theoretical fair spread (S*) as the ratio of these two terms –

the spread that would make the MTM equal zero.


Risk measurementsWhat are the problems?

Limited history – how do we capture risk for newly issued credit indices?

20−Dec−2004 20−Mar−2005 20−Jun−2005 20−Sep−2005 20−Dec−200535

40

45

50

55

60

65

70

75

80

Date

Spr

ead

(bp)

Series 3Series 4Series 5

Previous series?

On-the-run spreads?

Theoretical spreads?

Theoretical spreads plus basis?


What are the problems (cont’d)

Previous series / on-the-run spreadsEasy to use - single-name model with one time series – but …

Constituents are ignored (typical turnover is 5-10%)Difficult to stress names in hedged positions involving tranched CDOs

Risk numbers can be inaccurate – especially, when volatile names drop for a new issuance

Theoretical basket plus basisConstituent breakdown

Is the basis between the index spread and theoretical spread relevant?Basis volatility is significant

Correlation between basis and theoretical fair spread is low


Spread decomposition – the index basis

Decomposition of (quoted) spread

This decomposition allows us to create synthetic indices for short historiesEnsures that constituents are “fixed” (S* derived strictly from constituent CDS data)

Use on-the-run basis

Is S* good enough? Do we require the basis as a risk factor?

Theoretical fair spread

Basis: defined as the difference between the observed and theoretical fair spreads


Decomposition - Explaining the theoretical fair spread S*

Buying protection on the index is close to buying equal protection on each name, which would cost exactly SAVG , but S*≠SAVG

The biggest factor is heterogeneity. Consider the first default.Same loss payment, same notional reduction.Index buyer pays lower premium by index spread times notional reduction.Equal protection buyer pays lower premium by spread on defaulted name times notional reduction.

Larger spreads are those most likely to default.So equal protection buyer likely has a greater premium reduction than the index protection buyer.So index protection buyer should pay less at outset … S*<SAVG

The difference between the two can be interpreted as an indicator of heterogeneity


Why the basis?

Different quoting convention

Documentation differences (definition of default),

Maturity mismatches due to roll schedule and ISDA dates.

Different supply and demand effects,

Liquidity differences,

Asynchronous observations,

Preference for upfront (sure) versus running (risky) premiumHigher spreads … greater upfront payment to protection seller

Seller prefers upfront, so is willing to discount versus theoretical spread

Pushes observed spread lower … pushes basis lower (or more negative)


NAIG Series 3 spread decompositionBehavior of basis and nonlinearities in F/GM and Delphi events

20-Mar-2005 20-Jun-2005 20-Sep-2005 20-Dec-2005 20-Mar-2006 20-Jun-2006

30

40

50

60

70

80

90

Date

Spr

ead

(bp)

AverageNon LinearitiesBasisObserved

Ford and GMdowngrades

Delphidefault

Decrease ofdemand(old Series)


CDX.NAHY Series 4Less influence from default events


NAIG realized volatilitiesHow to estimate Series 5 risk on issuance date?

Series 3 includes F, GM, Delphi. Series 4 includes F, GM, not Delphi. Series 5 includes none.

20-Jun-2005 20-Sep-2005 20-Dec-2005 20-Mar-2006 20-Jun-2006

6

8

10

12

14

16

18

20

22

24

26

Date

Rea

lized

Vol

atilit

y ov

er 6

0 D

ays

(bp)

Series 3Series 4On-the-runSynthetic Series 5

Series 5


Agenda







Synthetic CDO mechanics

Protection buyer pays spread for protection against a portion of portfolio

losses

Typically, premium is paid as a spread on remaining notional over deal’s life

Underlying portfolio is a portfolio of single-name CDSs

Correlation is a key factor for pricing CDOsCorrelation does not affect the portfolio expected loss,

But redistributes losses around the capital structure


Tranche Pricing (standard version)

CDS price: deterministic discount factors, hazard rates

SCDO price: deterministic discount factors, hazard rates

What about loss distribution assumption?One-factor Gaussian copula is the market standard


Compound correlations are problematic

SCDO price is a function of:Asset correlation

CDS spreads

Maturity

Recovery rates

Compound correlation: Asset correlation inferred from SCDO priceMultiple solutions for mezzanine tranches

How do you price a tranche with non-standard attachment/detachment points?


Base correlation framework

Each tranche is decomposed into two “virtual” equity tranchesIncorporate entire capital structure

Why?Some analogy with pricing equity options with multiple strikes

Consistency across a fixed maturity (inconsistent across different tenors)

More importantly, empirical evidence suggests that base correlations provide better sensitivities than compound correlations.

From standard index tranches we can bootstrap base correlations

),(),( ,0,0, aabbba sVsVV ρρ −=


Stress tests

Base correlations can be stressed directly or indirectlyShift risk factors – user defined stress

Shift model parameters – generalized stress test

Indirect stresses involve market observables:Upfront fee of equity and junior tranches

Tranche fair spreads

Stresses should propagate up the capital structureEach stress shift involving market quotes is translated into a base correlation shift

Example:

0-3% Upfront fee increases bootstrap: calculate ρ3’

3-7% Tranche fair spread increases bootstrap: calculate ρ7’ (use ρ3’)

7-10% No stress is applied bootstrap: use ρ7’ (ρ10’ unaltered)


Stress test mechanics for model parameters

We can derive (bootstrap) market quotes in various ways

0-3% p1 s1 P1, sd1 pc1

3-7% p2 s2 P2, sd2 pc2

Tranche 1

Tranche 2

A/D Base Corr Fair spreadUpfront / deal spread Comp corr

0-3% p1 s1 P1, sd1 pc1

3-7% p2 s2 P2, sd2 pc2

Stress Test

Bootstrap base correlations when market observables are shifted

Calibrated parameters


Base correlation as a risk factorVolatility versus price level

iTraxx Europe (Jan-05 to Sept-07)

0.1 0.15 0.2 0.250

0.005

0.01

0.015

0.02

0.025

0.1 0.15 0.2 0.250.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Vol from absolute difference Vol from relative difference


Pricing bespoke tranches under the base correlation framework

What’s a bespoke tranche?Non-standard custom CDO trancheThe investor chooses:

Reference portfolioAttachment/detachment pointsMaturityOther details

Term used to distinguish SCDO tranches from (liquid) index tranchesTypically, refers to a different reference portfolio

It’s illiquidCan we use standard tranche indices to price and capture risk for bespokes?Standard index tranches:

CDX 0-3%, 3-7%, 7-10%, 10-15%, 15-30%iTraxx 0-3%, 3-6%, 6-9%, 9-12%, 12-22%


Mapping base correlations between bespoke and index portfolios

How do we price a bespoke tranche?Equivalently, how do we determine base correlations for a bespoke?

Given a base correlation surface ρΙ(X,T), can we determine ρΒ(X,T)?

Idea is to find an equivalent equity tranche on a standard index with strike XI

This mapping gives the bespoke base correlations:


Mapping base correlations:Mechanics after “equivalent” strike is determined

Consider a risky bespoke portfolio:

Bespoke portfolio Index portfolio

a

b

a’

b’

Iρ

a’ b’

)'()()'()(

aabb

IB

IB

ρρρρ

==

Index base correlations


Two mapping options are available

User-defined mappingUser explicitly enters the equivalent attachment/detachment points from the index portfolio

Expected tranche loss mappingEquivalent strikes between the bespoke and index portfolios are determined via an expected tranche loss calculation

Adjusting loss distribution implied by one-factor Gaussian copula


Summary

Credit indices – Basis as a risk factorThe basis matters, especially if you are trading it.

The basket constituents matter, even for large, safe indices.

A proxy based on synthetic histories can pick up both effects.

Synthetic CDOs – base correlation frameworkBase correlation are fairly straightforward to implement

Entire capital structure is incorporated (for the same maturity)

Stress testsProvide flexibility by allowing shifts of market observables

Fair spreads, upfront fees

Expected tranche loss is useful:Pricing of bespoke tranches

Future work: Interpolation / extrapolation of base correlations

Structured Credit Solutions in Practice

February 28, 2008

Marianela Hoz de Vila

[email protected]


Agenda

Analytic enhancementsCDS IndexSynthetic CDO

“Base Correlation Curve Spec”“Bespoke Tranche Mapping Method”“Zero Coupon Synthetic CDO”

Stress Test Base CorrelationsCredit Spread Market Observables

Fair Spread; Upfront Price

Reports


CDS Index - Overview

One input : CDS Index Spread Time Series


Synthetic CDO - Overview

Constituent SourceOne input : Index Spread Time Series

Issuer List: 125 names

Capital Structure


Synthetic CDO - Overview

Base Correlation Time series

Bespoke Tranches

Zero Coupon Synth CDO

Market Tranche List


Stress Test – Index Basis

CDS Spread Curve Shift

CDS Index Basis Shift


Stress Test – Base Correlation

Tranche Base Correlation Shift (Explicit)

CDO Base Correlation Shift (Explicit)

Fair Spread Shift (Implicit)

Compound Correlation Shift (Implicit)

Upfront Payment Shift (Implicit)


Reports – CDX Index VaR

..........


Reports – CDX Index Sensitivities


Reports – Synth CDO VaR

Base Correlation Risk

Bespoke Tranche


Reports – Synth CDO Sensitivities

Worst one-day move to CDX.NA.IG S8: July 25-26, 2007

CDX spread: +23%

Upfront fee: +15%

0-3% Base Correlation: +17%

Implicit Base Correlation Shift

Upfront Fee + Spread

Index is linked to all constituents


SummaryC

HA

LL

EN

GE

•Risk management in structured credit

EX

PO

SUR

ES

•Systemic risk (index spreads)•Idiosyncratic risk (single name defaults)•Correlation risk (often driven by market observables)

Measure and Manage Risk•Index spreads•Single name spreads•Correlation (across the entire capital structure)•Volatility (single name spreads AND correlations as risk factors!)

TO

OL

S


Questions

Please send any questions or comments to your Account Manager…

Date post:	12-Sep-2021
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

Structured Credit Solutions

Documents