Securitization 301

Securitization 301

Dynamic Structuring & Analysis

R&R Consulting

January 2006 R&R Consulting for the ASF -2-

US Capital Markets, 1970-1980s

Securitization (á la 101 )

DerivativesCorporate Finance

market risk

liqu

idity / cre

dit risk

ba

sis risk

operational risk

cash

synth

etics

cred

it risk Securitization?


Securitization 101

• Benchmark Pool (an adaptation of the corporate finance method)

• Back-of-the-Envelope (liquidation) Analysis (securitization)– Credit risk: value is a function of CE and

expected losses– Prepayment risk: to the extent it reduces CE– Counterparty risk: covers everything else


US Capital Markets, 1990s

Securitization (á la 101 or 201)

Derivatives

Corporate Finance

market risk

liqu

idity / cre

dit risk

ba

sis risk

operational risk

cash

synth

etics

Rated, repackagedmarket risk

cred

it risk


Securitization 201

• Scenario-Driven Cash Flow Analysis (securitization)– Credit risk: value is a function of CE and loss

volatility; prepayment risk embedded in the CF model

– Counterparty risk: covers everything else

• Monte Carlo Cash Flow Analysis (securitization)


US Capital Markets Now

Securitization (MC simulation)

Derivatives

Corporate Finance

ba

sis risk

operational risk

cash

synth

etics

Liq

uid

ity/cred

it risk

market risk


Securitization 301

• Monte Carlo Cash Flow Analysis (securitization)

– Credit risk: value is a function of CE and loss volatility; prepayment risk embedded in the CF model

– Servicer risk: has operational and credit dimensions

– Liquidity risk: was always there but is more highlighted

– Market risk: also highlighted for both accounting & portfolio management reasons

– Basis risk: may be part of the cash flow analysis

– Counterparty risk: do ratings really do the job?

• Option-Theoretic Valuation Framework

– Market risk: price is the goal. Fair value is a structural analysis; prices are a random walk

– Credit risk: value is approximated through a Merton default model; for credit portfolios, via a Gaussian copula

– Servicer risk: value is approximated through a Merton default model

– Liquidity risk: addressed in a market sense

– Counterparty risk: not quite on the radar screen.


The Drivers of Dynamic Analysis

Drivers of Change

• Economic efficiencies• Labor market pressures• Increased regulation

Market Effects of Change

• Commoditization of Risk• Competition of ideas• Market convergence


Technical Items in this Module

• The non-credit elements in the total analysis of payment certainty: liquidity, basis, market, operational risk

• The expanded set of performance metrics: volatility, correlation; duration, convexity

• The expanded set of solutions: contingent claims modeling; Monte Carlo simulation; Gaussian Copula

• Competitor paradigms of credit analysis

• The credit derivatives market: products, vocabulary, metrics of credit default modeling


Synthetic vs. Analytical Approaches

Causal EmpiricalWhere Cash securitization analysis Traditional "f inancial engineering"

How Rating agency & proprietary methods Option-theoretic framew orkWho Rating agencies Traders & "geeks"What Indepth analysis of unpublished Traded prices and other liability-side

asset-side performance data performance dataWhen With the payment periodicity Continuous

Why There is a unique solution There are many candidate solutions


Measures of Risk, by Domain

Term Measures DomainCredit Risk delinquency BACEN Resolution 2682; some securitizations

default rate credit baskets & single-names1-year loss rate credit from an accounting perspectivecumulative loss rate securitizationshistorical maxima corporation creditloss distribution securitizationscorrelation coeff icient credit portfolios

Liquidity Risk financial ratios credit generallyopen positions exchange-traded markets

Market Risk variance market & creditm. duration/convexity market

Basis Risk variance market (inter-market variation)Operational Risk informal market & credit

servicer ratings securitizations


Credit Risk

Measures currently in use:

(1) Default

– an estimate of the probability that a borrower will not repay all or a

portion of a loan on time (OTS);

– an ISDA credit definition;

– an empirical point-estimate taken from static pool history

– a random deviate from a distribution (or “guesstribution”)


Credit Risk (alt)

(2) Loss– an estimate of the shortfall on a financial contractual amount due (originally

signified assets, now also signifies liabilities) after recoveries are netted from defaults

– an input into the IRB risk-weighting model to produce a capital charge– an output of a Vasicek-type credit risk model– a point-estimate taken from static pool history– a statistical point-estimate on a logistic curve

(3) Reduction of Yield: difference between the sample average yields in a Monte Carlo simulation and a contractual or target yield.


Discussion

Rating agency ratings map all three types of measure to the alphanumeric rating. They are by no means interchangeable:

– They are unlike in their information efficiency: IRR is fungible, can be compared to other yields; E(L) has more information than defaults but it can be manipulated by changing the recovery assumption; Default-based analysis over-states high frequency/low severity events and understates low frequency/high severity events. It is the furthest from the cash flow analysis.

– Each produces a different numeric and a different rating:

Rating Class A Class BIRR AA+/Aa1 B+/B1

E(L) AA+/Aa1 BB/Ba2

Default AA+/Aa1 B-/B3


Liquidity Risk

The term specifies very different contexts:

• The risk of a company’s working capital becoming insufficient to meet near term financial demands. (Treasury Management Association of Canada)

• The risk associated with transactions made in illiquid markets. Such markets are characterized by wide bid/offer spreads, lack of transparency and large movements in price after a deal of any size. (Federal Home Loan Bank of Dallas)


Market Risk

• Risk associated with fluctuations in (asset) prices (Minnesota Mutual)

• The possibility that the price of a security will change over time (David Gerster)

• A random walk, or, equivalently, Geometric Brownian motion

Most simply written

where the first term signifies the expected rate of change with respect to time and the second term signifies deviations from the first term that are normally distributed “error” terms.

Prices in equilibrium are assumed to move as

dXdtP

dP

rtePtP 0)(


Basis Risk

A risk that the value of the financial instrument does not move in line with the underlying exposure. Generally, it refers to an imperfect hedge where the matched risk-offsetting positions are not in identical markets (Capital Market Risk Advisers)

Generally presumed to be less risky than outright market risk exposure—but data granularity is important. When the markets stop moving in tandem, the magnitude of risk is outside expectation.

),cov(2

)()()(

22 yx

yExEzE

yxz


Operational Risk

• According to §644 of International Convergence of Capital Measurement and Capital Standards, known as Basel II, operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events. (Wikipedia)

• …Operational risk may be defined by what it does not include: market risk, credit risk, and liquidity risk. (CMRA)


credit controlservicer staying pow er xxx x

management experience x xxw orkflow design & structure of compensation xxx

quality & capacity of the team xxinformation management x xxx

internal audit x xxxplatform security x xx

How Well Do Servicer Ratings Benchmark Operational Risk?


Definitions: Volatility

• A measure of the fluctuation in the market price of the underlying security. Mathematically, volatility is the annualized standard deviation of returns. (optiondigest.com)

• If the average quarterly asset price volatility is 25%, annualized price volatility is

• If the average one-year price volatility is 25%, daily price volatility is

221 ixn

4%25

252

%25


Applications - Volatility

Credit Risk: used to contextualize the microstructure of E(L) variability in structured securities. Theoretical—not substantiated by empirical data in real applications.

Market Risk: the exogenous input in a Black-Scholes model for valuing contingent claims on market risk exposures.

Basis Risk: the exogenous input in a Black-Scholes model for valuing contingent claims on basis risk exposures.


Definitions: Correlation

The word is used in two different senses:

“If I hold two securities and one defaults, what is the likelihood that the other will also default?”

Strictly speaking, this is not correlation but conditional probability. It takes on a range of values [0,1], reflecting only positive correlation.

The common statistical measure of correlation is the Pearson correlation coefficient, a number with a range of [-1,1],

This reflects diversification as well as interdependence. It should not be confused with causality, however.

ji

jjiiij

xx

)])([(

)(

),()(

i

jiji xP

xxPxxP


Critical Applications - Correlation

Credit Risk: used to quantify the interdependence of risk exposures in credit portfolios and the impact on cash flow certainty: CDOs, credit basket trades.


Definitions: Modified Duration

• Measures the sensitivity of bond prices to changes in rate environment

• As a first derivative of price with respect to yield, it gives a rough indication of how much price will rise (fall) for a small unit change

• Begin with price:

• Take the first derivative with respect to yields:

• To normalize the output, divide the result by P.

Although duration is approximately correct for small changes, due to the non-linear relationship between price and yield, it is not very accurate for larger changes.

T

tt

tt r

CP

1 )1(

tT

tt

tT

tt rtC

rrtC

r

P

1

)1(

11

1

1

1


Convexity

• Measures the sensitivity of price to changes in rate environment

• As the second derivative of price with respect to yield, it shows the magnitude of sensitivity of the change in price to the change in yield

T

tt

t

r

ttC

rr

P

1

2

22

2

)1(

)(

)1(

1


Modified Duration/Early Repayment

• When the call date is certain, Effective Duration provides a linear adjustment to Modified Duration that averages the asymmetrical price impact of rising or falling rates:

• Effective Duration is not a good approximation when the call date is uncertain. Prepayment ability by the borrower (a call option) turns cash flows that are fixed into a cash flow that is itself a function of interest rates:

, for a vector of cash flows, Ct(r).

• The algebra of duration and convexity become more complex with cash-flow dependency. The formula for modified duration becomes:

rP

PP du

02

T

tt

tt r

rCP

1 )1(

)(

n

ii

iiii

r

rCrir

rCr

D1

2

1

1

)(1)(

1


Definition: Gaussian Copula


Definitions: Recoveries

The definition of recoveries is trivial: 1-lgd (loss-given-default)

The problem is one of data quality, or perhaps it should be called data scrupulousness.


Impact of Prepayments on Value

Some bonds, like MBS, have a tendency to prepay in some interest rate environments.

The tapering off of interest (and principal) cash flows only impairs their creditworthiness to the extent it affects XS, but it has adverse consequences for reinvestment or trading activity.

I need a way to price a callable bond that reflects the impact of prepayment risk.


Price Sensitivity to Yield Change

Modified Duration

$0

$25

$50

$75

$100

$125

$150

$175

$200

1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

YTM (%)

Bo

nd

Pri

ce How actual prices change

Price estimates


Negative Convexity

$0

$20

$40

$60

$80

$100

$120

$140

$160

1 2 3 4 5 6 7 8 9 10 11Yield (%)

Pri

ce (

$)

Non-Callable

Callable


Interest vs. PPMT Cash Flows

$-

$1,000,000

$2,000,000

$3,000,000

$4,000,000

$5,000,000

$6,000,000

$7,000,000

1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267 281 295 309 323 337 351

Time

$-

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

$12,000,000

$14,000,000

$16,000,000

1 16 31 46 61 76 91 106 121 136 151 166 181 196 211 226 241 256 271 286 301 316 331 346

Time

PSA0%

50%100%200%400%


PACs and TACs


Problem: Valuing Rights of Ownership

Rights of ownership (contingent claims) are not the same as outright ownership.

Intuitively, the value of contingent claims is a random variable that should rise when price volatility increases and fall when time-to-expiration amortizes.

I need a consistent method for pricing an ownership right in the “pre-ownership” phase.


Contingent Claims Valuation

• Single-most influential valuation concept in modern finance. Sprenkel published the first general approach in the 1960s, which did not rely on risk neutrality.

• Fischer Black and Myron Scholes published their arguments for a closed form solution to the problem of valuing contingent assets using the heat diffusion equation.

• Black-Scholes facilitates pricing uncertain cash flows by transforming them into risk-neutral equivalents through a process of continuous re-hedging. The approach rests on certain simplifying assumptions (next page, pls)

• The fundamental insight underlying risk-neutral pricing is the put-call parity condition, where S = asset price, P is the price of a put, C, is the price of a call, and Ee-r(T-t) is the price of a risk-free loan:

CEePS tTr )(


Black-Scholes Assumptions

• The risk-free rate, dividends and asset volatility can be known over the life of the exposure

• The hedge costs are de minimus

• The asset trades continuously (short or long positions are both possible) and it is divisible

• The marketplace responds instantaneously to new information (efficient market hypothesis) to form a rational price; deviations from the equilibrium price are random


Black-Scholes Modeling

Critical Applications

Market Risk: the consensus fair value metric for pricing futures, options and structured derivative trades (swaps, collars, caps) in organized and OTC exchanges. Aspects of the underlying argument are actively used in establishing and maintaining market risk-neutral positions. Continuous trading is an operational requirement. A central clearing and settlement function is highly desirable from the standpoint of credit risk elimination.

Credit Risk: used in structural (Merton default) models to establish an implied default risk of a corporation. Fundamental insight is the characterization of residual value as a call on the company assets and the insolvency boundary as a put on the company assets back to the lender.

Other applications: (1) Borrowers who refinance their mortgage loans before maturity are said to be long a “call option” with respect to the loan, which they can exercise if interest rates go down (price goes up/call option is “in the money”). An implied price for these securities can be worked back to from a back-of-the-envelope calculation on the value of the borrower’s call. (2) Sellers of default protection (CDS) are said to go long the probability of corporate default on the reference obligation of the firm and buyers of default protection are said to be short the probability of corporate default on the same.


Problem: Process Modeling without a Closed Form Solution

Black-Scholes uses the heat-transfer equation to describe the dissipation of errors.

What if there is no known analogue from physics or engineering that I can use to model the financial process?

I need a way to use what I know about the past to condition my expectations on the future.


Monte Carlo Simulation

• Multiple sampling from a real portfolio is impossible. Hence the usefulness of sampling from a theoretical universe.

• If we could draw a suitably large number of samples from the theoretical universe reflecting the underwriting criteria of the loans in question, we could perform parametric statistical analysis on the samples, and use the results to structure a transaction.

One method of simulation, the Inverse Distribution Function Method (IDFM), can be performed in spreadsheets using Excel functions, or in Visual Basic for Excel. Assume an initial cumulative loss distribution:

Flipping coins on the y-axis using a random number generator to find the cumulative frequency of occurrence (the left-hand term in the equation below) a corresponding loss is drawn (the right-hand term).

Flipping many such coins to draw many will eventually populate the original distribution , by the law of large numbers.

dyyfxF )()(

ij xyF )(1

dxxfxF i )()(


Inverse Distribution Function Method

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0%

1

85

169

253

337

421

505

589

673

757

841

925

1009

1093

1177

1261

1345

1429

1513

1597

1681

1765

1849

1933

2017

2101

2185

2269

2353

2437

91% of the probability mass


Monte Carlo Simulation

Critical Applications

Credit Risk: used by some rating agencies to rate asset-backed or mortgage-backed securities or CDOs, to rate transactions. MC simulation allows the impact of the microstructure of risk on the payment certainty of structured securities to be measured systematically with probability-weighted scenarios.

Market Risk: used in Option Adjusted Spread (OAS) calculations. The difference between the theoretical price of the MBS and what MBS investors are willing pay can be evaluated in cash flow terms. This is the bond’s “option-adjusted spread” or OAS.


OAS Modeling

• Simulates sequences of interest rate paths to produce a set of cash flows and an average life, for each security in the structure. Three main building blocks:

– Interest rate model, used to generate a set of rate paths that are inputs to the next block. Rate paths need to be as long as the longest maturity of any loan in the MBS pool.

– Prepayment rate model using rate paths produced in Step 1 to produce cash flows. Prepayment models are “conditional” in the sense that they attempt to predict prepayment rates given interest rates and other driver variables, instead of trying to predict these independent variables themselves.

– Cash flow model able to combine the prepayment rates from Step 2 and compute the OAS spreads by reference to market bond prices and the yield curve. Schematically, the OAS methodology can be visualized in the figure below.

Yield Curve

(current coupon)

Rate Volatility

Assumptions

Interest RateModel

(MC Scenarios)

PrepaymentModel

(PPMT Vector)

Cash Flow Model(P&I)

OAS,Duration,Convexity


Problem: Sizing the Cash Flow Impact of Correlation on Credit Portfolios

I know how to calculate correlation coefficients, but what kind of data should I use?

I need a way to systematically stress a portfolio of exposures to reflect the impact of sectoral inter- and intra-dependence.


Technical Content

• Non-credit elements in the total analysis of payment certainty: basis, market, operational risk

• Solutions and the expanded set of performance metrics and methods: volatility, correlation; duration, convexity; contingent claims modeling; Monte Carlo simulation; Gaussian Copula.

• Competitor paradigms for credit analysis

• The credit derivatives market: products, vocabulary, metrics of credit default modeling for buying & selling pure default risk.


Alternative Credit Paradigms

• Structural (Merton Default)• Intensity (Hazard Rate) Modeling


Technical Content

• The non-credit elements in the total analysis of payment certainty: basis, market, operational risk.

• Solutions and the expanded set of performance metrics and methods: volatility, correlation; duration, convexity; contingent claims modeling; Monte Carlo simulation; Gaussian Copula

• Competitor paradigms.of credit analysis

• The credit derivatives market: products, vocabulary, metrics of credit default modeling for buying & selling pure default risk


Credit Synthetics

• Are not securitizations under Reg AB• Are said to facilitate separation of risk management, funding

roles• International Swaps & Derivatives Association (ISDA) provides

transaction governance structure: contracts, confirmations, legal opinions, key definitions, day count conventions, settlement procedures

• Basic valuation framework is cash-and-carry trade• More sophisticated modeling alternatives: structural, intensity

models


Product Typology

CDS CLN CSO TRS CDO BasketsAsset Composition single-name single-name single-name single-name ~80-300 ~125Capital Structure reference flexible reference reference flexible fixed

Strategy Traded OBS Funded OnBS Traded OBS Used as CE Traded OBS Traded OBSUsed as CE Dealer hedge Investor hedge Funded OnBS

Dealer hedgeInvestor hedge


New Risks Come into Focus

• Swap replacement risk

• Swap settlement risk

• Physical delivery risk

• Cash-Synthetic basis risk


Where do we go from here?


Derivatives

Corporate Finance

ba

sis risk

operational risk

cash

synth

etics

Liq

uid

ity/cred

it risk

market risk


Hypothesis: Inversion of the pre-1990 Market Structure


Derivatives

Institutions

ba

sis risk

operational risk

cash

synth

etics

Liq

uid

ity/cred

it risk

market risk

Innovation, policy risk

Securitization 301

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