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					                                                CDO Option
                                                Market Model
A CDO Option Market Model for                     DORN J.

standardized CDS Index Tranches                 Preliminaries
Conference on Numerical Methods in Finance      Motivation
                                                Recall : CDO
                                                Structure
                                                CDO Spread
                                                Determinants
                                                Previous
                  Jochen DORN                   Research

                                                The Model
                                                Overview
                PRISM Research Center           Option Pay-Off
                  Finance Department            Spread Dynamics

          Université Paris1 Panthéon-Sorbonne   Conclusion

                                                Implementation

                  April 16th 2009
                                                          CDO Option
Economic Motivation                                       Market Model

                                                            DORN J.

Market Context                                            Preliminaries

    CDO is a OTC Product ⇒ High Transaction Costs         Motivation
                                                          Recall : CDO
                                                          Structure

    "Liquidity Gap" costs precious Basis Points           CDO Spread
                                                          Determinants
                                                          Previous
                                                          Research
⇒ Initialization of a standardized synthetic CDO Market   The Model
(CDX/iTraXX)                                              Overview
                                                          Option Pay-Off
                                                          Spread Dynamics

                                                          Conclusion

                                                          Implementation
                                                              CDO Option
Economic Motivation                                           Market Model

                                                                DORN J.

Market Context                                                Preliminaries

    CDO is a OTC Product ⇒ High Transaction Costs             Motivation
                                                              Recall : CDO
                                                              Structure

    "Liquidity Gap" costs precious Basis Points               CDO Spread
                                                              Determinants
                                                              Previous
                                                              Research
⇒ Initialization of a standardized synthetic CDO Market       The Model
(CDX/iTraXX)                                                  Overview
                                                              Option Pay-Off
                                                              Spread Dynamics

Modeling Constraints                                          Conclusion

                                                              Implementation
    Credit Derivatives : "Static" Models ⇒ The investor
    does not pay for the Véga !
    Pricing of CDO tranches with option alike pay-offs (Deal
    Spread, Cumulative Loss as underlying)
    "Maturity Trap"
→ need for Spread Dynamics !
                                                        CDO Option
Objectives                                              Market Model

                                                          DORN J.


                                                        Preliminaries
                                                        Motivation
                                                        Recall : CDO
                                                        Structure
                                                        CDO Spread
                                                        Determinants
                                                        Previous
                                                        Research
   We consider a CDO tranche with AP D% and DP E %
                                                        The Model
   and tenor [Ta ; Tb ].                                Overview
                                                        Option Pay-Off
   The aim consists in finding a recursive formula for   Spread Dynamics


   market-implied Spread Dynamics !                     Conclusion

                                                        Implementation
   ⇒ need for liquid market data.
                                                           CDO Option
                                                           Market Model

                                                             DORN J.

Standardization Assumptions
                                                           Preliminaries
    Underlying CDS Portfolio restricted to components of   Motivation
                                                           Recall : CDO
    CDX / iTraXX index series                              Structure
                                                           CDO Spread
                                                           Determinants
    Pre-Set Attachment / Detachment Points                 Previous
                                                           Research


→ Success Story ⇒ option trading possible                  The Model
                                                           Overview
                                                           Option Pay-Off
                                                           Spread Dynamics

                                                           Conclusion

                                                           Implementation
                                                           CDO Option
                                                           Market Model

                                                             DORN J.

Standardization Assumptions
                                                           Preliminaries
    Underlying CDS Portfolio restricted to components of   Motivation
                                                           Recall : CDO
    CDX / iTraXX index series                              Structure
                                                           CDO Spread
                                                           Determinants
    Pre-Set Attachment / Detachment Points                 Previous
                                                           Research


→ Success Story ⇒ option trading possible                  The Model
                                                           Overview
                                                           Option Pay-Off
                                                           Spread Dynamics
CDS Index Tranches                                         Conclusion

    CDS Index Tranches securitize CDS Index Series.        Implementation


    Attachment / Detachment Points are standardized
    [0%, 3%, 6%, 9%, 12%, 22%, 100%]
    ⇒ improves liquidity, reduces ramp-up costs for
    structurers
                                                                                                        CDO Option
Synthetic CDO Structure                                                                                 Market Model

   Only synthetic CDOs (CDOs on a CDS portfolio) allow                                                    DORN J.

   for product standardization and hence for liquidity                                                  Preliminaries
   CDOs securitize credit spreads and issue tranches →                                                  Motivation
                                                                                                        Recall : CDO
   Leverage                                                                                             Structure
                                                                                                        CDO Spread
                                                                                                        Determinants
                                                                                                        Previous
                                                                                                        Research

                                                                                                        The Model
                                                                                                        Overview
                                        Systemic Risk                                                   Option Pay-Off
                                                                                                        Spread Dynamics




                                                                                      Increasing Risk
                                                                                                        Conclusion
                                                                           Senior
                                                                           EUR 850m                     Implementation
                          Swap                    Interest &
                          Premium                 Principal
     CDS Reference Pool
                                       SPV
        100 names
                                                   Funding
            X             Protection
     EUR 10m notional     Payment
            =                                                             Mezzanine
                                                      Decreasing Spread




       EUR 1000m
                                                                           EUR 850m
      Total otional




                                                                           Equity
                             Idiosyncratic Risk                            EUR 50m
                                                   CDO Option
Recall CDO Spread Determinants                     Market Model

                                                     DORN J.


                                                   Preliminaries
                                                   Motivation
                                                   Recall : CDO
                                                   Structure
                                                   CDO Spread
Definition "CDO Premium Leg" :                     Determinants
                                                   Previous
                                                   Research
   Sum of discounted Cash-Flows perceived by the   The Model
   Trancheholder                                   Overview
                                                   Option Pay-Off
                                                   Spread Dynamics

                                                   Conclusion

                                                   Implementation
                                                               CDO Option
Recall CDO Spread Determinants                                 Market Model

                                                                 DORN J.


                                                               Preliminaries
                                                               Motivation
                                                               Recall : CDO
                                                               Structure
                                                               CDO Spread
Definition "CDO Premium Leg" :                                 Determinants
                                                               Previous
                                                               Research
   Sum of discounted Cash-Flows perceived by the               The Model
   Trancheholder                                               Overview
                                                               Option Pay-Off
                                                               Spread Dynamics

Definition "CDO Protection Leg" :                              Conclusion

   Sum of the discounted reductions of a tranche’s notional    Implementation

   inherent to credit events which lead to a decrease in the
   Trancheholder’s "spread revenue".
                                                                 CDO Option
                                                                 Market Model

Definition "Fair Spread" :                                         DORN J.

    The t-time Fair Spread is the Spread the investor should     Preliminaries
    have contracted instead of Deal Spread + Euribor/Libor       Motivation
                                                                 Recall : CDO
    at issuing date in order to allow the tranche quote at par   Structure
                                                                 CDO Spread

    at time t.                                                   Determinants
                                                                 Previous
                                                                 Research

                                                                 The Model
                             Protection Leg                      Overview
               Fair Spread =                                     Option Pay-Off
                             Premium Leg                         Spread Dynamics

                                                                 Conclusion
Notional Erosion → Spread has to be calculated on the            Implementation
outstanding Tranche Notional
                                                                 CDO Option
                                                                 Market Model

Definition "Fair Spread" :                                         DORN J.

    The t-time Fair Spread is the Spread the investor should     Preliminaries
    have contracted instead of Deal Spread + Euribor/Libor       Motivation
                                                                 Recall : CDO
    at issuing date in order to allow the tranche quote at par   Structure
                                                                 CDO Spread

    at time t.                                                   Determinants
                                                                 Previous
                                                                 Research

                                                                 The Model
                             Protection Leg                      Overview
               Fair Spread =                                     Option Pay-Off
                             Premium Leg                         Spread Dynamics

                                                                 Conclusion
Notional Erosion → Spread has to be calculated on the            Implementation
outstanding Tranche Notional
Definition Forward Fair Tranche Spread

                            B(t, Ti )Protection Legi
       Fwd Fair Spread =
                             i B(t, Ti )Premium Legi
                                                              CDO Option
History of Market Models in                                   Market Model

Derivatives                                                     DORN J.


The BGM Model (Brace-Gatarek-Musiela)                         Preliminaries
                                                              Motivation

   Arbitrage-Free model for other than instantaneous,         Recall : CDO
                                                              Structure
                                                              CDO Spread
   continuously compounded forward rates                      Determinants
                                                              Previous
                                                              Research
   The idea is to chose a different numeraire other than the   The Model
   risk-free account                                          Overview
                                                              Option Pay-Off

   Leads to Black’s formula → we refer to as "market          Spread Dynamics

                                                              Conclusion
   models"
                                                              Implementation
   First attempt to model a market-implied term structure
   of forward rates
                                                              CDO Option
History of Market Models in                                   Market Model

Derivatives                                                     DORN J.


The BGM Model (Brace-Gatarek-Musiela)                         Preliminaries
                                                              Motivation

   Arbitrage-Free model for other than instantaneous,         Recall : CDO
                                                              Structure
                                                              CDO Spread
   continuously compounded forward rates                      Determinants
                                                              Previous
                                                              Research
   The idea is to chose a different numeraire other than the   The Model
   risk-free account                                          Overview
                                                              Option Pay-Off

   Leads to Black’s formula → we refer to as "market          Spread Dynamics

                                                              Conclusion
   models"
                                                              Implementation
   First attempt to model a market-implied term structure
   of forward rates
CDS Option Market Model
   Brigo & Mercurio transferred the idea of a market
   model into the credit derivatives environment
   One-Period Spread modeling approach applied to the
   CDS market, with approximation constraints
                                                                                            CDO Option
The Model - Central Idea                                                                    Market Model

                                                                                              DORN J.


                                                                                            Preliminaries
                                                                                            Motivation
                                                                                            Recall : CDO
                                                                                            Structure
                         Describe a fwd-start option on a synth.                            CDO Spread
                          CDS Index Tranche (B&S framework)                                 Determinants
                                                                                            Previous
                                                                                            Research

                                  Possibility to select any                                 The Model
                                  mtgle dynamics of the                                     Overview
                                  fwd spread rate under                                     Option Pay-Off
       Define forward Fair         associated probability
                                                              The Expected outstanding      Spread Dynamics
       Tranche Spread as a                measure              Tranche Notional is a t-
                                                                                            Conclusion
    function of the numeraire                                  fwd neutral martingale
                                                                                            Implementation




                                                              Calculate its volatility in
     Derive forward spread
                                                               function of the Spread
     dynamics for different
                                                              Rate and the associated
         time horizons
                                                                observable volatility
                                                                    CDO Option
A closed-form Market Formula                                        Market Model

                                                                      DORN J.
Lemma
Let ΠCallCDO D,E (t, K ) describe the t−time pay-off of a            Preliminaries
              a,b                                                   Motivation

forward start call option written on standardized CDO               Recall : CDO
                                                                    Structure
                                                                    CDO Spread
tranche with boundaries [D%; E %]. The tenor is [Ta ; Tb ].         Determinants
                                                                    Previous
Within the Black & Scholes framework the Call option takes          Research

                                                                    The Model
the value                                                           Overview
                                                                    Option Pay-Off

                       ˆ D,E       D,E
ΠCallCDO D,E (t, K ) = Ca,b (t) × Sa,b (t)N(d1 ) − K × N(d2 )
                                                                    Spread Dynamics

                                                                    Conclusion
        a,b
                                                                    Implementation

with
                                b
          ˆ D,E
          Ca,b (Ta ) =:                            t
                                    δi B(Ta , Ti )EQ Ti [X (Ti )]
                            i=a+1
                      D,E
                     Sa,b (t)                     T
                ln      K        ± (Ta − t) 1 t a σa,b (s)ds
                                            2
                                                   2

       d1,2 =                            √
                            σa,b (Ta − t) Ta − t
                                                      CDO Option
Step 1- The Fwd Spread Dynamics                       Market Model

                                                        DORN J.
Definition                   Fwd-neutral Measure
                                                      Preliminaries
                                                      Motivation
                                 D,E
   D,E         Protleg (t)     dQa,b        ≈
                                                      Recall : CDO
                                                      Structure
  Sa,b (t)   =                         =              CDO Spread
               Premleg(t)       dQ       Premleg(t)   Determinants
                                                      Previous
                                                      Research

                                                      The Model
                                                      Overview
                                                      Option Pay-Off
                                                      Spread Dynamics

                                                      Conclusion

                                                      Implementation
                                                      CDO Option
Step 1- The Fwd Spread Dynamics                       Market Model

                                                        DORN J.
Definition                   Fwd-neutral Measure
                                                      Preliminaries
                                                      Motivation
                                 D,E
   D,E         Protleg (t)     dQa,b        ≈
                                                      Recall : CDO
                                                      Structure
  Sa,b (t)   =                         =              CDO Spread
               Premleg(t)       dQ       Premleg(t)   Determinants
                                                      Previous
                                                      Research

                                                      The Model
                                                      Overview
                                                      Option Pay-Off
                                                      Spread Dynamics

                                                      Conclusion

                                                      Implementation
                                                              CDO Option
Step 1- The Fwd Spread Dynamics                               Market Model

                                                                DORN J.
Definition                          Fwd-neutral Measure
                                                              Preliminaries
                                                              Motivation
                                         D,E
   D,E         Protleg (t)             dQa,b        ≈
                                                              Recall : CDO
                                                              Structure
  Sa,b (t)   =                                 =              CDO Spread
               Premleg(t)               dQ       Premleg(t)   Determinants
                                                              Previous
                                                              Research

                                                              The Model
                                                              Overview
                                                              Option Pay-Off
                                                              Spread Dynamics

                                                              Conclusion

                                                              Implementation




           D,E           D,E
    Hence Sa,b (t) is a Qa,b - martingale.
      D,E
    dSa,b (t)
     D,E         = σa,b (t)dWta,b
    Sa,b (t)
    Yi −1 (t)
     Yi (t)     introduces recursion
                                                          CDO Option
Step 2 - Shortfall Dynamics                               Market Model

                                                            DORN J.
Corollary
The expected outstanding tranche notional Yi (t) is a     Preliminaries
                                                          Motivation
Q t -martingale. Its dynamics under the forward-neutral   Recall : CDO
                                                          Structure

probability Q t follows :                                 CDO Spread
                                                          Determinants
                                                          Previous
                                                          Research
                     dYi (t)                              The Model
                             = γi (t)dZt
                     Yi (t)                               Overview
                                                          Option Pay-Off
                                                          Spread Dynamics

                                                          Conclusion

                                                          Implementation
                                                              CDO Option
Step 2 - Shortfall Dynamics                                   Market Model

                                                                DORN J.
Corollary
The expected outstanding tranche notional Yi (t) is a         Preliminaries
                                                              Motivation
Q t -martingale. Its dynamics under the forward-neutral       Recall : CDO
                                                              Structure

probability Q t follows :                                     CDO Spread
                                                              Determinants
                                                              Previous
                                                              Research
                       dYi (t)                                The Model
                               = γi (t)dZt
                       Yi (t)                                 Overview
                                                              Option Pay-Off
                                                              Spread Dynamics

                                                              Conclusion
Step 3 - Deriving the Volatility                              Implementation


Lemma
∀k ∈ [a + 1; b] the volatility of the process Yk related to
tenor [Ta , Tb ] is given by
                       k           D,E
                               δj Sj−1,j (t)
        γk (t) = −                   D,E
                                                 σj−1,j (t)
                     j=a+1   1 + δj Sj−1,j (t)
                                                                                   CDO Option
Step 4 - The Fwd one-period Spread                                                 Market Model

Dynamics                                                                             DORN J.


Corollary                                                                          Preliminaries
                                                                                   Motivation
Consider a deal with tenor [Ta , Tb ] and tranche [D, E ]. The                     Recall : CDO
                                                                                   Structure

dynamics of the forward one-period Fair Tranche Spread on                          CDO Spread
                                                                                   Determinants
                                                                                   Previous
tenor [Ti−1 , Ti ] is given by :                                                   Research

                                                                                   The Model
  D,E                           i                D,E                               Overview
dSi−1,i (t)                                  δj Sj−1,j (t)                         Option Pay-Off

  D,E
              = σi−1,i (t)ρ                        D,E
                                                               (σj−1,j (t))   dt   Spread Dynamics

Si−1,i (t)                    j=a+1      1   + δj Sj−1,j (t)                       Conclusion

                                                                                   Implementation
              + σi−1,i (t)dZt

More precisely, for a deal with tenor [Ti−1 , Ti ], the forward
one-period Fair Tranche Spread dynamics for the same tenor
amounts to :
    D,E                   D,E
  dSi−1,i (t)         δi Si−1,i (t)
   D,E
                =           D,E
                                        |σi−1,i (t)|2 dt + σi−1,i (t)dWt
  Si−1,i (t)        1 + δi Si−1,i (t)
                                                                   CDO Option
Step 5 - The Multi-Period Extension                                Market Model

                                                                     DORN J.

Lemma                                                              Preliminaries

Again consider a deal with tenor [Ta , Tb ] and tranche [D, E ].   Motivation
                                                                   Recall : CDO
                                                                   Structure
The forward multi-period spread dynamics with the same             CDO Spread
                                                                   Determinants
             D,E
tenor, note Sa,b , can be written as                               Previous
                                                                   Research

                                                                   The Model
    D,E
  dSa,b (t)                                                        Overview
                                                                   Option Pay-Off

    D,E
              = (Λ(t) + ς(t)) ρ (Λ(t)) dt − (Λ(t) + ς(t)) dZt      Spread Dynamics

  Sa,b (t)                                                         Conclusion

                                                                   Implementation

with
                    b
                          δi A(t, Ti )Yi (t)
         Λ(t) =                              γi (t)
                  i=a+1       C D,E (t)
                              ˆ
                                a,b
                           A(t, Tb )Yb (t)
         ς(t) =                                     γb (t)
                  A(t, Ta )Ya (t) − A(t, Tb )Yb (t)
                                                                    CDO Option
Conclusion                                                          Market Model

   Market Model allows for calibration of options with                DORN J.

   bespoke exercise periods to options with more liquid             Preliminaries
   tenors thanks to multi-period fwd Tranche Spread                 Motivation
                                                                    Recall : CDO
   Dynamics ⇒ More realistic prices.                                Structure
                                                                    CDO Spread
                                                                    Determinants
                                                                    Previous
                                                                    Research

                                                                    The Model
                                                                    Overview
                                                                    Option Pay-Off
                                                                    Spread Dynamics
          T_a                    T_b               Illiquid Tenor
                                                                    Conclusion

                                                                    Implementation




                  T_c                        T_d   Liquid Tenor
                                                            CDO Option
Conclusion                                                  Market Model

                                                              DORN J.


                                                            Preliminaries
                                                            Motivation
                                                            Recall : CDO
                                                            Structure
                                                            CDO Spread
                                                            Determinants

   Possibility of pricing options on tranches with future   Previous
                                                            Research

   ramp-up dates ⇒ Fwd spread is no longer a martingale     The Model
                                                            Overview
   ⇒Calculate expectations of the fwd spread dynamics !     Option Pay-Off
                                                            Spread Dynamics

   Fwd spread dynamics allow for modeling of deals with     Conclusion

   complicated pay-offs !                                    Implementation

   The investor finally pays for the Véga !
                                                                                                                           CDO Option
Implementation (1)                                                                                                         Market Model

                                                                                                                             DORN J.


                                                                                                                           Preliminaries
                                                                    Ta =4,Tb =5
                                                                                                                           Motivation
                                                                                                                           Recall : CDO
                                                                                                                           Structure
                                                                                                                           CDO Spread
                    4
                 x 10                                                                                                      Determinants
           2.5                                                                                                             Previous
                                                                                                                           Research

                                                                                                                           The Model
            2
                                                                                                                           Overview
                                                                                                                           Option Pay-Off
                                                                                                                           Spread Dynamics
           1.5

                                                                                                                           Conclusion
    call




            1                                                                                                              Implementation


           0.5



                                                                                                                       1
            0
            0                                                                                                    0.8
                   0.1
                         0.2                                                                               0.6
                               0.3
                                     0.4                                                    0.4
                                           0.5
                                                 0.6
                                                        0.7                           0.2
                                                              0.8
                                                                     0.9
                                                                              1   0
                                                                                                  correl

                                                  tranches




                        Fig.: Call Value based on 4y - 5y Spreads.
                                                                                                                               CDO Option
Implementation (2)                                                                                                             Market Model

                                                                                                                                 DORN J.


                                                                                                                               Preliminaries
                                                                    Ta =8,Tb =9
                                                                                                                               Motivation
                                                                                                                               Recall : CDO
                                                                                                                               Structure
                                                                                                                               CDO Spread
                                                                                                                               Determinants
                    4                                                                                                          Previous
                 x 10
                                                                                                                               Research
           2.5

                                                                                                                               The Model
            2
                                                                                                                               Overview
                                                                                                                               Option Pay-Off
                                                                                                                               Spread Dynamics
           1.5
                                                                                                                               Conclusion
    call




            1                                                                                                                  Implementation

           0.5


                                                                                                                           1
            0                                                                                                        0.8
            0
                   0.1
                         0.2                                                                                   0.6
                               0.3
                                     0.4                                                        0.4
                                           0.5
                                                 0.6
                                                        0.7                               0.2
                                                              0.8
                                                                      0.9
                                                                                  1   0
                                                                                                      correl

                                                  tranches




                        Fig.: Call Value based on 8y - 9y Spreads.
                                                                                                                              CDO Option
Implementation (3)                                                                                                            Market Model

                                                                                                                                DORN J.


                                                                                                                              Preliminaries
                                                                 Ta =1,Tb =2
                                                                                                                              Motivation
                                                                                                                              Recall : CDO
                                                                                                                              Structure
                    5
                 x 10
                                                                                                                              CDO Spread
            2                                                                                                                 Determinants
           1.8
                                                                                                                              Previous
                                                                                                                              Research
           1.6
                                                                                                                              The Model
           1.4
                                                                                                                              Overview
           1.2
                                                                                                                              Option Pay-Off
            1                                                                                                                 Spread Dynamics
    call




           0.8
                                                                                                                              Conclusion
           0.6

           0.4
                                                                                                                              Implementation
           0.2

            0
            1

                        0.8

                              0.6                                                                                         1
                                                                                                                    0.9
                                                                                                              0.8
                                             0.4                                                        0.7
                                                                                                  0.6
                                                                                            0.5
                                                   0.2                               0.4
                                                                               0.3
                                                                         0.2
                                                         0       0.1
                                                             0
                                    correl
                                                                                     tranches




   Fig.: Cumulative Call Value based on 1y - 2y Spreads.
                                                                                                                                  CDO Option
Implementation (4)                                                                                                                Market Model

                                                                                                                                    DORN J.


                                                                                                                                  Preliminaries
                                                   Tj =2,Ti =15,Tranche(%) = [0.5,0.6],correl =0.09
                                                                                                                                  Motivation
                                                                                                                                  Recall : CDO
                   4
                x 10
                                                                                                                                  Structure
           5
                                                                                                                                  CDO Spread
                                                                                                                                  Determinants
                                                                                                                                  Previous
           4                                                                                                                      Research

                                                                                                                                  The Model
           3
                                                                                                                                  Overview
                                                                                                                                  Option Pay-Off
           2                                                                                                                      Spread Dynamics
    call




                                                                                                                                  Conclusion
           1

                                                                                                                                  Implementation
           0



           -1
            0

                       500
                                                                                                                             16
                               1000                                                                                     14
                                                                                                                   12
                                                                                                              10
                                           1500                                                   8
                                                                                     6
                                                                        4
                                                  2000     2
                                                                                               time horizon
                                  iterations




                             Fig.: Converging one-period spreads.
                                                                                                                                                        CDO Option
Implementation (5)                                                                                                                                      Market Model

                                                                                                                                                          DORN J.


                                                                                                                                                        Preliminaries
                                                                  differences(closed form - monte carlo)T a = 1,Tb = 6
                                                                                                                                                        Motivation
                                                                                                                                                        Recall : CDO
                                                                                                                                                        Structure
                                                                                                                                                        CDO Spread
                                                                                                                                                        Determinants
    1500
                                                                                                                                                        Previous
                                                                                                                                                        Research
    1000
                                                                                                                                                        The Model
     500
                                                                                                                                                        Overview
                                                                                                                                                        Option Pay-Off
       0
                                                                                                                                                        Spread Dynamics
     -500
                                                                                                                                                        Conclusion
    -1000
                                                                                                                                                        Implementation
    -1500
       1
            0.9
                  0.8
                        0.7
                              0.6
                                                                                                                                                  0.9
                                    0.5                                                                                                     0.8
                                          0.4                                                                                         0.7
                                                                                                                                0.6
                                                0.3                                                                       0.5
                                                      0.2                                                          0.4
                                                                                                         0.3
                                                            0.1                               0.2
                                correl                                              0.1
                                                                   0      0
                                                                                                               tranches




    Fig.: Differential Closed-form formula vs. Dynamics.
                                                          CDO Option
Outlook                                                   Market Model

                                                            DORN J.


                                                          Preliminaries
                                                          Motivation
                                                          Recall : CDO
                                                          Structure
                                                          CDO Spread
                                                          Determinants
   Approach might serve to model bespoke CDOs.            Previous
                                                          Research

   The spread on a CDO tranche can be replicated by a     The Model
                                                          Overview
   Call Spread on the CDO’s cumulative Loss Given         Option Pay-Off
                                                          Spread Dynamics
   Default (LGD) with strikes being the respective
                                                          Conclusion
   Attachment/Detachment Points.                          Implementation
   Hence by modeling the LGD dynamics there should be a
   way to price bespoke CDO tranches.
                                 CDO Option
                                 Market Model

                                   DORN J.


                                 Preliminaries
                                 Motivation
                                 Recall : CDO
                                 Structure
                                 CDO Spread
                                 Determinants
                                 Previous
                                 Research


THANK YOU FOR YOUR ATTENTION !   The Model
                                 Overview
                                 Option Pay-Off
                                 Spread Dynamics

                                 Conclusion

                                 Implementation

				
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