Securitization 301 - American Securitization Forum by pengtt

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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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