This document discusses the basics of synthetic CDOs including: how they transfer credit risk from an originator to investors through an SPV without actual asset transfer; the difference between cash and synthetic CDO structures; typical synthetic CDO structures using credit default swaps; and types of synthetic CDOs such as unfunded, funded, and partially funded. It also covers motivation for synthetic CDOs, risk factors associated, and how ratings agencies model and analyze synthetic CDOs.

1. Synthetic CDO XLRI Jamshedpur HimadriSingha(019) Kumar Vikram (024) HozefaBharmal(078) Group 3 RituAgarwal (102) Subhadip Das (110) Nikhil Uppal (092)

2. Basics of Synthetic CDO This product was introduced where Credit Risk Transfer was more important Credit Risk is transferred by Originator to the Investors by means of CD instruments Risk transfer is undertaken by an SPV Originator is the “Protection Buyer” and Investors are “Protection Seller” Main purpose is to mitigate risk without any asset transfer.

3. Cash CDO Vs Synthetic CDO Cash CDO Involve a portfolio of cash assets (corporate bonds) Ownership of assets is transferred to SPV, issuing the tranches SPV bears the operational risk Synthetic CDO Do not own cash assets These CDOs gain exposure only to the assets through CDS. SPV doesn’t bear the operational risk

4. Synthetic CDO Structure Default Payment P & I SPV (Protection Seller) Coupon Payment Proceeds CDS Premium Trustee High Quality Asset

5. Waterfall Diagram CDS Premium Default Payment Low Risk Senior Tranche Low Yield Mezzanine Tranche High Risk Equity High Yield

7. Protection seller’s payment obligation is not paid upfront

8. Investors are ultimate protection seller.

9. Funded Synthetic CDO

10. Protection seller’s payment obligation is paid upfront through issuing CLN

11. Proceeds from CLN are invested in Risk Free assets

13. Funded Synthetic CDO Interest payment equal to the yield on high quality asset + CDS Premium Default Payment SPV (Protection Seller) Coupon LIBOR + X bps Proceeds CDS Premium From CLN Trustee This is done to “delink” the credit ratings of the notes from the rating of the originator. Else downgrade of the originator would downgrade the issued notes. Notes equal to 100% of the value of the ref pool of assets are issued High Quality Asset

14. Partially Funded Synthetic CDO Unfunded Tranche Funded Tranche SST does not pay purchase price. Rather SST receives payments as protection seller and is liable to pay the originator if the underlying assets suffer a loss above specified level. Perceived risk is less 5-10% default risk Super Senior Protection CDS Premium Pay if default SPV (Protection Seller) CDS Premium Coupon Libor+ X bps Proceeds Pay if default From CLN Trustee High Quality Asset

15. A typical funding structure

16. Motivation Typically the reference assets are not actually removed from the sponsoring firm’s balance sheet. For this reason: Synthetic CDOs are easier to execute than cash structures the legal documentation and other administrative requirements are less burdensome Synthetic CDO ensures transfer of credit risk of assets not suited for conventional securitization, while the actual assets are retained on the balance sheet. For example, Bank guarantees, Letter of Credit etc. A more efficient way of Credit risk mitigation Originator does not have to reduce book size as BS remains unchanged The super senior tranche, which prices well below a typical AAA tranche and which makes up more than 80% of the synthetic CDO, is a major driver of the economics of the synthetic CDO

17. Motivation Cash Flow CDO 1 billion dollar Reference Portfolio Synthetic CDO 1 billion dollar Reference Portfolio That means if CDO manager can reinvest in collateral pool risk free asset at, say, (LIBOR-5 bp), it is able to gain from a savings of 20 bp on each 100 dollar if structure is unfunded A Considerable Gain

18. Structure of a CDO Tranche Traditionally, a collateralized debt obligation pool is divided into three tranches; wherein each tranche behaves as a separate CDO, enabling the CDO originators to attract multiple investors having varying risk preferences 1. Senior Tranche or Senior Debt: This is typically highly rated, since it is ranked on top in terms of priority of payments. However, the interest rate on investments in this tranche is the lowest due to the lower risk that accompanies them 2. Mezzanine Tranche: This tranche has moderate returns and moderate risk 3. Equity Tranche: Investment in this tranche yields the highest interest rate. This high rate is offered to counter the higher risk on this tranche. Equity tranche investors are the first to lose funds when loans in the pool are not repaid

20. Asset Classes

21. Portfolio diversity and rating

22. Portfolio geographical and industrial variation

23. Portfolio term to maturity

24. Type of collaterals used

26. The CDO manager sells only a single tranche – usually at the mezzanine level – of the capital structure to an investor instead of selling all the tranches at the same time

29. Due to the absence of a true sale of the underlying assets, synthetic CDOs involve the credit risk inherent in the underlying assets. These assets could be bonds, ABS, MBS, loans etc. The risk of these assets is generally measured using their credit rating, historical performances and any other asset specific information.

30. Legal issues associated with the CDO definition

31. As there is a conflict of interest between the protection buyer and the protection seller on the occurrence of a credit event it is of prime importance that the “trigger events” be clearly defined.

32. Counterparty credit risk

34. and Reference Portfolio must comply,

35. Appoint the Protection Buyer itself as calculation agent (who determines whether or not a Credit Event has occurred) and

36. Give a supervising role to the Protection Buyer’s external auditors.Tax Issues Since the title of the reference Obligations are not transferred to the Protection Seller, taxation is not a major consideration in the case of a Synthetic CDO

37. Moody’s Ratings Framework Moody's rating on each rated note represents the expected loss on the note, which is the difference between the present value of the expected payments on the note and the present value of the promised payments under the note, expressed as a percentage of the present value of the promise To evaluate the expected loss, Moody’s incorporates both quantitative and qualitative analysis Moody's expected loss models capture the quantifiable risks while a legal review of the transaction seeks to ensure that non-quantifiable risks are mitigated through documentation provisions

38. Quantitative Analyses The primary source of risk in a synthetic CDO comes from the reference pool Moody’s uses the quantitative analysis to assess the risks stemming from the reference pool The premium payments are excluded from the scope of the quantitative analysis because the promised premium is large enough to ensure coverage of the interest payments on the CDO There are two primary methods to model a default risk: Binomial Expansion Modeling Multiple Binomial Modeling

39. Binomial Expansion Modeling Primarily used for a pool of homogeneous assets A model portfolio is created which contains a pool of Ndiversity bonds Each diversity bond is assumed to have identical characteristics in terms of par/notional amount, rating, average life, spread and recovery, and is uncorrelated with every other diversity bond in the pool The number of diversity bonds in the portfolio is equivalent to Moody's diversity score

40. Binomial Expansion Modeling The losses stemming from the default of each additional diversity bond in the model portfolio going from zero diversity bond defaults to N diversity bond defaults is calculated and a probability assigned to each default scenario Calculating this probability-weighted loss for each CDO tranche generates the expected loss

41. Multiple Binomial Modeling An extension of the Double Binomial Method, used in cases where the underlying portfolio assets exhibit heterogeneous characteristics - such as having a clear delineation between low rated and highly rated assets Moody’s divides a pool of reference entities/credits into the most appropriate number of sub-pools and models the default behavior of each pool with a separate binomial analysis Each diversity bond is assumed to have identical characteristics in terms of par/notional amount, rating, average life, spread and recovery, and is uncorrelated with every other diversity bond in the pool

42. Multiple Binomial Modeling The mathematical expression for the multiple binomial-based expected loss used by Moody’s is as below:

43. Multiple Binomial Modeling Factors which warrant the use of the Multiple Binomial Method to quantify the inherent risks are: Portfolio Characteristics Most synthetic CDOs have reference entities/credits whose ratings can vary greatly (typically Aaa down to Baa3 or even Ba3), for a 5-year synthetic CDO, Moody's idealized default probability can vary from as little as 0.003% for a Aaacredit to 3.05% for a Baa3 credit and 11.86% for a Ba3 credit

44. Multiple Binomial Modeling Capital Structure Most synthetic CDOs are highly leveraged and are thus sensitive to fewer defaults than cash flow CDOs .Hence only a small amount of subordination is necessary to support high ratings. This thin subordination combined with the relatively small sizes of the rated tranches generally requires more precision in the calculation of the tail probability of the loss distribution. Structural Features, or Lack Thereof Many synthetic CDOs do not have the ability to generate any excess spread that may be used to offset losses in the reference pool. Hence, it is even more important to capture the correct loss distribution when analysing the expected loss of a CDO tranche

45. Qualitative Analysis In case risks inherent in a synthetic CDO are not or cannot be modeled quantitatively, they would be addressed through the legal documentation, and hence the importance of Qualitative Analysis The important aspects of the qualitative analysis unique to synthetic CDOs can be grouped into three main categories: Trading guidelines for managed synthetic CDOs Credit event definitions and their effects on the modeled default probabilities Structural features such as valuation procedures and settlement mechanisms that affect recovery rate assumptions.

46. NIG for Synthetic CDO Pricing Normal Inverse Gaussian Distribution for Synthetic CDO pricing is an extension of the popular Large Homogeneous Portfolio (LHP), approach to CDO pricing LHP assumes a flat default correlation structure over the reference credit portfolio and models defaults using a 1-factor Gaussian copula This model leads to an implied correlation skew, as it fails to fit the prices of different CDO tranches simultaneously This is explained by the lack of tail dependence in the Gaussian copula and a Student t-distribution is proposed However, the t-distribution leads to an increase in computation time and therefore the NIG is proposed

47. NIG for Synthetic CDO Pricing Normal Inverse Gaussian Distribution is a special case of the generalized hyperbolic distribution They are flexible four parameter distribution family that can produce fat tails and skewness

48. Properties of NIG Normal Inverse Gaussian Distribution is a mixture of the normal and the inverse Gaussian distributions They are flexible four parameter distribution family that can produce fat tails and skewness A non-negative random variable Y has an Inverse Gaussian distribution with parameters: Hence

49. Properties of NIG A random variable X follows a Normal Inverse Gaussian Distribution with parameters They density and probability functions are thus:

50. Properties of NIG The main properties of the NIG distribution class are the scaling property: And the closure under convolution for independent random variables X and Y:

51. Derivation of Pricing formula using NIG: Since M does not depend on a, we set: The random variable, Is NIG distributed and its parameters are:

52. Derivation of Pricing formula using NIG: Thereafter the 3rd and 4th parameters are restricted to standardize the distributions of both the factors: With

53. Derivation of Pricing formula using NIG: Starting with: Then applying the scaling property we get: Thereafter applying the convolution property to

54. Derivation of Pricing formula using NIG: Finally, we get: The above is the expression for the NIG distribution function and the density

56. Leads to lower transaction cost as SPV setup cost can be avoided

57. Use of credit derivatives offer greater flexibility for risk requirement

58. Cost of buying protection is lower and credit protection price is below the note liability

59. Range of reference asset is wider and typically includes bank guarantee, derivative instruments

60. Clients whose loans need not be sold off from the sponsoring agent’s B/S can be better handled and leads to improved customer relationship

62. Common method is to use average rating of the reference portfolio which consists of 150 or more reference names

64. Because correlation is unobservable, differences of opinion among market participants as to the correct default correlation creates trading opportunities

65. Diversity score of a CDO plays a part in calculating the precise correlation value which is used to map the underlying CDO portfolio into a hypothetical portfolio consisting of homogeneous assets

67. However, for synthetic CDOs with credit default swap as assets in the portfolio, this factor needs to be ignored

68. Analyst performs simulation model to generate scenarios of default and expected returns

69. All variables like the number of defaults swap to maturity, recovery rates and timing of defaults etc. are considered as random and thus modeled using stochastic process

70. However, actual recovery rates might differ based on the macroeconomic factors