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Securitization 301
Dynamic Structuring &
Analysis
R&R Consulting
US Capital Markets, 1970-1980s
market risk
credit risk
basis risk
liquidity / credit risk
Securitization Securitization?
(á la 101 )
cash
Corporate Finance Derivatives
synthetics
operational risk
January 2006 R&R Consulting for the ASF -2-
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
January 2006 R&R Consulting for the ASF -3-
US Capital Markets, 1990s
market risk
basis risk
credit risk
liquidity / credit risk
Rated,
repackaged
Securitization market risk
(á la 101
or 201)
cash
Corporate Finance
synthetics
Derivatives
operational risk
January 2006 R&R Consulting for the ASF -4-
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)
January 2006 R&R Consulting for the ASF -5-
US Capital Markets Now
market risk
basis risk
Liquidity/credit risk
Securitization
(MC simulation)
cash
Corporate Finance
synthetics
Derivatives
operational risk
January 2006 R&R Consulting for the ASF -6-
Securitization 301
• Monte Carlo Cash Flow • Option-Theoretic Valuation
Analysis (securitization) Framework
– Credit risk: value is a function of – Market risk: price is the goal. Fair
CE and loss volatility; prepayment value is a structural analysis; prices
risk embedded in the CF model are a random walk
– Servicer risk: has operational and – Credit risk: value is approximated
credit dimensions through a Merton default model; for
– Liquidity risk: was always there credit portfolios, via a Gaussian
but is more highlighted copula
– Market risk: also highlighted for – Servicer risk: value is approximated
both accounting & portfolio through a Merton default model
management reasons – Liquidity risk: addressed in a market
– Basis risk: may be part of the cash sense
flow analysis – Counterparty risk: not quite on the
– Counterparty risk: do ratings really radar screen.
do the job?
January 2006 R&R Consulting for the ASF -7-
The Drivers of Dynamic Analysis
Drivers of Change Market Effects of Change
• Economic efficiencies • Commoditization of Risk
• Labor market pressures • Competition of ideas
• Increased regulation • Market convergence
January 2006 R&R Consulting for the ASF -8-
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
January 2006 R&R Consulting for the ASF -9-
Synthetic vs. Analytical Approaches
January 2006 R&R Consulting for the ASF -10-
Measures of Risk, by Domain
January 2006 R&R Consulting for the ASF -11-
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‖)
January 2006 R&R Consulting for the ASF -12-
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.
January 2006 R&R Consulting for the ASF -13-
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:
January 2006 R&R Consulting for the ASF -14-
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)
January 2006 R&R Consulting for the ASF -15-
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
January 2006 R&R Consulting for the ASF -16-
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.
January 2006 R&R Consulting for the ASF -17-
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)
January 2006 R&R Consulting for the ASF -18-
How Well Do Servicer Ratings
Benchmark Operational Risk?
January 2006 R&R Consulting for the ASF -19-
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
January 2006 R&R Consulting for the ASF -20-
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
January 2006 R&R Consulting for the ASF -21-
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.
January 2006 R&R Consulting for the ASF -22-
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.
January 2006 R&R Consulting for the ASF -23-
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.
January 2006 R&R Consulting for the ASF -24-
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.
January 2006 R&R Consulting for the ASF -25-
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
January 2006 R&R Consulting for the ASF -26-
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:
January 2006 R&R Consulting for the ASF -27-
Definition: Gaussian Copula
January 2006 R&R Consulting for the ASF -28-
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.
January 2006 R&R Consulting for the ASF -29-
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
January 2006 R&R Consulting for the ASF -30-
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.
January 2006 R&R Consulting for the ASF -31-
Price Sensitivity to Yield Change
How actual prices change
Price estimates
January 2006 R&R Consulting for the ASF -32-
Negative Convexity
January 2006 R&R Consulting for the ASF -33-
Interest vs. PPMT Cash Flows
January 2006 R&R Consulting for the ASF -34-
PACs and TACs
January 2006 R&R Consulting for the ASF -35-
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.
January 2006 R&R Consulting for the ASF -36-
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:
January 2006 R&R Consulting for the ASF -37-
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
January 2006 R&R Consulting for the ASF -38-
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.
January 2006 R&R Consulting for the ASF -39-
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.
January 2006 R&R Consulting for the ASF -40-
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.
January 2006 R&R Consulting for the ASF -41-
Inverse Distribution Function Method
91% of the probability mass
January 2006 R&R Consulting for the ASF -42-
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.
January 2006 R&R Consulting for the ASF -43-
OAS Modeling
• Simulates sequences of interest rate paths
to produce a set of cash flows and an Rate Yield
average life, for each security in the Volatility Curve
structure. Three main building blocks: Assumptions
(current coupon)
– 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 Interest Rate
maturity of any loan in the MBS pool. Model
– Prepayment rate model using rate paths
produced in Step 1 to produce cash flows. (MC Scenarios)
Prepayment models are ―conditional‖ in the
sense that they attempt to predict prepayment
rates given interest rates and other driver Prepayment
variables, instead of trying to predict these
independent variables themselves. Model
– Cash flow model able to combine the (PPMT Vector)
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. Cash Flow Model
(P&I)
OAS,
Duration,
Convexity
January 2006 R&R Consulting for the ASF -44-
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.
January 2006 R&R Consulting for the ASF -45-
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.
January 2006 R&R Consulting for the ASF -46-
Alternative Credit Paradigms
• Structural (Merton Default)
• Intensity (Hazard Rate) Modeling
January 2006 R&R Consulting for the ASF -47-
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
January 2006 R&R Consulting for the ASF -48-
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
January 2006 R&R Consulting for the ASF -49-
Product Typology
January 2006 R&R Consulting for the ASF -50-
New Risks Come into Focus
• Swap replacement risk
• Swap settlement risk
• Physical delivery risk
• Cash-Synthetic basis risk
January 2006 R&R Consulting for the ASF -51-
Where do we go from here?
market risk
basis risk
Liquidity/credit risk
Securitization
(MC simulation)
cash
Corporate Finance
synthetics
Derivatives
operational risk
January 2006 R&R Consulting for the ASF -52-
Hypothesis: Inversion of the pre-1990
Market Structure
market risk
basis risk
Liquidity/credit risk
Securitization
(MC simulation)
cash
Innovation, policy risk
Institutions
synthetics
Derivatives
operational risk
January 2006 R&R Consulting for the ASF -53-
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