Securitization 301

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Securitization 301

• Dynamic Structuring Analysis

RR Consulting
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US Capital Markets, 1970-1980s
market risk
Securitization (á la 101 )
Derivatives
Corporate Finance
basis risk
credit risk
Securitization?
liquidity / credit risk
cash
synthetics
operational risk
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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

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US Capital Markets, 1990s
market risk
Securitization (á la 101
or 201)
Corporate Finance
basis risk
Rated, repackaged market risk
credit risk
liquidity / credit risk
cash
Derivatives
synthetics
operational risk
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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)

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US Capital Markets Now
market risk
Securitization (MC simulation)
Corporate Finance
basis risk
Liquidity/credit risk
cash
Derivatives
synthetics
operational risk
7
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.

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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

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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

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Synthetic vs. Analytical Approaches
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Measures of Risk, by Domain
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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)

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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.

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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

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Liquidity Risk

• The term specifies very different contexts
• The risk of a companys 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)

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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

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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 exposurebut data
  granularity is important. When the markets stop
  moving in tandem, the magnitude of risk is
  outside expectation.

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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)

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How Well Do Servicer Ratings Benchmark
Operational Risk?
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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

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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

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Applications - Volatility

• Credit Risk used to contextualize the
  microstructure of E(L) variability in structured
  securities. Theoreticalnot 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.

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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.

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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.

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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.

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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

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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

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Definition Gaussian Copula
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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.

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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

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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.

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Price Sensitivity to Yield Change
How actual prices change
Price estimates
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Negative Convexity
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Interest vs. PPMT Cash Flows
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PACs and TACs
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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.

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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

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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

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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 borrowers 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.

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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.

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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.

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Inverse Distribution Function Method
91 of the probability mass
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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 bonds
  option-adjusted spread or OAS.

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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 Rate Model (MC Scenarios)
Prepayment Model (PPMT Vector)
Cash Flow Model (PI)
OAS, Duration, Convexity
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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.

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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.

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Alternative Credit Paradigms

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

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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

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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

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Product Typology
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New Risks Come into Focus

• Swap replacement risk
• Swap settlement risk
• Physical delivery risk
• Cash-Synthetic basis risk

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Where do we go from here?
market risk
Securitization (MC simulation)
Corporate Finance
basis risk
Liquidity/credit risk
cash
Derivatives
synthetics
operational risk
53
Hypothesis Inversion of the pre-1990 Market
Structure
market risk
Institutions
Securitization (MC simulation)
basis risk
Liquidity/credit risk
cash
Innovation, policy risk
Derivatives
synthetics
operational risk