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A Study of Sellers of Senior Tranched Credit Protection

A Study of Sellers of Senior Tranched Credit Protection. Jon Gregory Quant Congress USA July 8 th 2008. Related Papers. “ Credit Tails ”, Risk article, January 2008 “ A Trick of the Credit Tail ”, Risk technical paper, March 2008

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A Study of Sellers of Senior Tranched Credit Protection

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  1. A Study of Sellers of Senior Tranched Credit Protection Jon Gregory Quant Congress USA July 8th 2008

  2. Related Papers “Credit Tails”, Risk article, January 2008 “A Trick of the Credit Tail”, Risk technical paper, March 2008 “A Free Lunch and the Credit Crunch”, to be published August 2008 “Two Faced Over Counterparty Credit Risk?”, working paper Please email me at jon-gregory@supanet.com for copies of these articles

  3. The Failure of the Gaussian Copula Model Gaussian Copula Model Market Super Senior 22-100% 3.53 0.05 8.75 6.99 14.0 32.9 12-22% 26.5 82.0 9-12% 82.5 234.7 6-9% 3-6% 24.00% 19.3% Equity 0-3% • Dependency is defined by a single correlation parameter • No concept of idiosyncratic default • No concept of systemic default

  4. CDO Investor Landscape Risk of underlying [15-30%] And [30-100%] Aaa rated Monolines and CDPCs no CSA Super Aaa [10-15%] Aaa Real money investors under CSA [7-10%] Aa [3-7%] Baa Hedge funds [0-3%] NR Rating of counterparty

  5. The Correlation Skew in Credit Super Senior 22-100% Index [0-100%} 5Y iTraxx Europe (Investment Grade Corporate Index) 110 bps 12-22% 9-12% 6-9% 3-6% Equity 0-3% [0-3%] 35% [3-6%] 465 bps [6-9%] 335 bps [9-12%} 250 bps [12-22%] 110 bps [22-100%] 40 bps

  6. Into the Super Senior Space Super Senior 22-100% 12-22% 9-12% 6-9% 3-6% Equity 0-3% Each default causes loss of (1-)/125 = 0.48% (40% rec) 22% of losses requires 22% / 0.48% = 46 defaults 5Y [22-100%] pays around 50 bp pa ! Long protection on 7Y [22-100%] (Delta hedged)

  7. The Toothpaste Tube Analogy (I) Super Senior 22-100% Index [0-100%] 12-22% 9-12% 6-9% 3-6% • Index = Sum of tranches • [22-100%] = [0-100%] – [0-3%] – [3-6%] – [6-9%] – [9-12%] – [12-22%] Equity 0-3% • Typically method for extracting super senior premium implicitly assumes flat correlation curve up to 5Y

  8. Summary of Super Senior Pricing • We can’t price [22-60%] • We can’t price tranchelets in the [22-60%] region • We can’t price bespoke super senior

  9. The Toothpaste Tube Analogy (II) • Small changes in equity duration assumptions can change the size of the tube • Upper bound where [22-100%] is equal to [12-22%] / Lower bound where [22-100%] is worth zero • Change in 3Y equity premium (or IO/PO prices) moves super senior significantly Upper bound

  10. Extrapolation of Base Correlation Curve • Even if we can price the [22-100%] • Pricing of 1% wide tranchelets in the [22-60%] region • Clearly not arbitrage-free • No value put in the [1-, 100%] part of the capital structure ( is 40% in this case)

  11. Pricing of Bespoke Super Senior • Forced index tranchlets to be arbitrage-free (value distributed equally within [22-60%]) • On a portfolio which is 14% more risky, common scaling techniques introduce arbitrage • On a more risky portfolio this potentially becomes worse bespoke index

  12. Packaging Super Senior Risk • Leveraged super senior (LSS) trades • A leveraged transaction with a defined trigger event • Credit derivative product companies (CDPC) • Like a more complex LSS • Trigger is not so well defined • CDPC has multiple counterparties • Monoline insurer • Similar to CDPC but will insurer other financial risks also • Should benefit from diversification

  13. Leveraged Super Senior Illustration • Super senior tranche pays small premium • Leverage this (typically around 10 times) • Create a structure paying a ‘good’ premium referenced to a default remote tranche • Investor loss will come when structure deleverages • Investor may have option to post more collateral • Alternatively an unwind will occur Uncollateralized Portion Collateral × Leverage

  14. Rating Super Senior Risk Super senior tranche (Triple-A) • Packaging super senior tranches can always be made to look like triple-A counterparty risk Capital (share) of monoline / CDPC etc () Packaged Super senior tranche (at least Triple-A)

  15. LSS Unwind Triggers Loss only trigger Simple to rate (default risk only, like a CDO tranche) Issuer retains spread and implied correlation risk Spread (+ loss) triggers More complex to rate (includes spread dynamics in rating model) Issuer retains implied correlation risk Market value triggers Very hard to rate (only one rating agency DBRS have ever done so) Issuer retains only gap risk

  16. Leveraged Super Senior Pricing Argument There is around $200+ billion of leveraged super senior protection out there Issuers seem to price via the equivalence argument Advantage is that we simple argue that gap risk is very small Example : at 10 times leverage, a market value trigger of 5% is ‘safe’ This is a standard argument applied to lots of leveraged products (CPPI etc, ….) This argument is wrong for LSS LSS Protection value = SS Protection value  Leverage – Gap Risk

  17. LSS Protection Valuation Bounds [A, B] Upper Bound “Gap Risk” LSS Value?? × L Perfect trigger No trigger [A, A+] Lower Bound

  18. LSS Pricing Denote trigger time by initial collateral by No Standard tranche protection Trigger ? Yes Settle contract with cap at collateral value

  19. LSS Pricing (II) Collateralised Protection = 0 De-leverage value Even if client has option to deleverage then it is suboptimal Unwind value Gap option

  20. Formal Valuation • Setting de-leverage term to zero Lower Bound Trigger Option

  21. Leveraged Super Senior Overview Perfect trigger [A, B] Upper Bound “Gap Risk” Actual LSS Value “Trigger Option” No trigger [A, A+] Lower Bound

  22. Pricing the Trigger Option • Pricing (and hedging!) the trigger option is not easy • Out of the money tranche option payoff • But we can get some insight in the loss only trigger case • Here we can overhedge with a contract paying  at the loss trigger K • This is simply a digital CDO tranche • This effectively sets a maximum leverage independent of gap risk

  23. Example • For the (5Y) tranche markets as shown • We calculation the maximum leverage for • A [22-100%] LSS structure • 5-year maturity • With a loss trigger as a function of loss trigger level

  24. Maximum Leverage • Leverage Super Senior Pricing is not a gap risk problem!

  25. Monolines and CDPCs • Capital model • (Tranche) Ratings driven run on a daily basis • Capital (less any losses) must be above capital required by model to support Aaa rating • Operating modes (CDPC / monoline) • Normal operating mode / Triple-A rating • Suspension mode / downgrade • Wind-down mode / Run-off Ratings driven loss distribution Aaa attachment Required capital

  26. Monoline / CDPC Comparison with LSS Monoline / CDPC Leverage Super Senior Trigger Not Hit Normal State De-leverage Restricted State Trigger Hit < 6 months Wind-down State Full Deleverage (unwind) Losses to tranches Losses to tranches

  27. CDPC / Monoline Purchased Protection [A, B] Upper Bound “Counterparty Risk” [A, A+] Lower Bound for LSS Impact of effective leverage No value

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