## _wp06254 - References

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---

### I. Introduction — research questions and context
- CDS mechanics and credit events:
  - Protection buyer pays periodic premium until maturity or a predefined credit event.
  - Typical sovereign CDS contracts under ISDA allow restructuring as a credit event; triggers include (i) change in coupon rates, (ii) change in principal amount, (iii) postponement of interest or principal payment date, (iv) change in ranking of priority, (v) change in payment of interest or principal to a nonpermitted currency.
  - Physical delivery of the cheapest-to-deliver (CTD) bond occurs within 30 business days after a credit event.
- Key empirical motivations:
  - Distressed market trading and CTD squeezes can raise the actual recovery value relevant to protection buyers.
  - Soft restructurings in sovereign markets can imply actual recovery values as high as 60 percent, contrasting with analysts’ rule-of-thumb of using 25 percent to value CDS contracts under risk neutrality.
- Research questions:
  - Whether the choice of recovery value affects CDS pricing when delta-hedging with cash bonds; the offset between recovery assumption and implied default probability can break down when bond prices trade far below par.
  - Whether information on expected recovery values can be extracted from CDS data to guide pricing in future distress situations; empirical extraction illustrated for the Brazil crisis of 2002–03.
- Observed relationships and implications:
  - For deeply distressed bonds:
    - bond-implied default intensity increases exponentially with the recovery fraction of par value, as do CDS spreads;
    - CDS premiums (insurance on par) must exceed risk premia implied by bonds trading below par.
  - In soft restructurings, implied recovery values correlate closely with current distressed cash bond price levels; CDS-implied recovery rates can therefore be much higher than traditional assumptions.

### II. CDS valuation framework and mathematical foundation
- Premium leg and protection leg:
  - Buyer pays annual premium c per one unit of notional until maturity or a credit event; premium payments normally quarterly, at times t1,...,tN.
  - Premium leg present value given by integral/sum expression using continuous risk-free rate tr and risk-neutral intensity tλ.
  - Protection leg present value integrates expected post-default payment: protection buyer receives difference between par and market value of eligible bond; accrued interest  and expected fractional recovery of face value ω̂ enter expressions.
  - Fair premium t c chosen so premium leg equals protection leg at origination (equation (4) in source).
- Modeling features preserved:
  - Default time τ and settlement delay dτ (normally 30 business days) referenced.
  - Recovery of face value (RFV) notation: ω(dτ) and accrued interest A(dτ); present-value-at-default forms ω̂ and Â.
  - Fractional accrued premium 4* c appears in payoffs at default (equation (2) in source).
- Pricing implications:
  - CDS pricing depends critically on assumed recovery concept (RFV versus RMV) and on relation between bond prices and implied default intensity.
  - When bonds trade far below par, the usual offset between assumed recovery and implied default probability fails, altering CDS spreads materially.

### III. The basis: reasons for CDS vs bond spread divergence
- Definition:
  - Basis = CDS spread − corresponding point on the term structure curve of bond spreads; positive basis when CDS premiums exceed bond spreads.
- Conceptual and practical drivers:
  - Positive-basis drivers:
    - Delivery option: protection buyer can deliver any acceptable bond and receive par value.
    - Issuance of new bonds: pushes up demand for insurance, raising protection price.
    - Short selling abilities: CDS spreads can react faster to deteriorations as insurance demand increases.
    - Repo specialness: repurchase agreements on deliverable bonds can increase CDS spreads because such bonds are unavailable for delivery.
  - Negative-basis drivers:
    - Counterparty risk: premium compensates for protection seller default risk.
    - Bond illiquidity: illiquid paper often trades at higher spreads, reducing the basis (effect can be ambiguous).
    - Funding risk: protection seller does not incur funding risk that would arise if replicating the swap by buying the underlying funded at the risk-free rate.
- Empirical notes:
  - Many basis effects are difficult to detect empirically; delivery option often small when a single CTD dominates.
  - In distress episodes (Argentina, Uruguay, Brazil), long-maturity or yen-denominated low-coupon issues often served as CTD.
  - Liquidity proxies (bid-ask spread, principal amount) are significant in explaining basis for investment-grade corporates (Longstaff, Mithal, and Neis (2005)).
  - Contractual differences around restructuring clauses matter: contracts allowing restructurings can have up to a 7 percent higher CDS spread compared with no-restructuring (NR) contracts; analysis here restricts to contracts with full restructuring to avoid bias.
- Nontechnical mitigation channels:
  - Recovery swaps and post-delivery handling (e.g., netting, tear-ups like TriOptima) can reduce exposures; market participants providing recovery swaps include banks and dealers.

### Box 2 — Nontechnical basis effects and examples
- Nontechnical drivers of large CDS-bond basis:
  - Squeeze on certain bonds stemming from debt management (example: Brazil, August–September 2002 — squeeze on very short maturity, high-yield ‘04s and eligible interest (“EI”) bonds).
  - Repo specialness (example: Argentina, around December 2001 — local banks closed short positions by repo-ing certain bonds at 15 percent, below the regulator’s 24 percent penalty, removing bonds from the market and leaving fewer deliverable bonds after the credit event).
  - Central bank actions (example: Brazilian central bank bought most of the Brazilian yen bonds) can further squeeze CTD supply and raise CDS spreads.
- Evidence on repo specialness and short-position closing:
  - Argentina anecdote: repo transactions at 15 percent removed bonds used as collateral, reducing deliverable supply after a credit event and magnifying CDS basis.

### The role of recovery in CDS-bond basis (conceptual summary)
- Distinct recovery measures:
  - CDS recovery measure: risk-neutral recovery of face value insured by the CDS contract, denoted ω (RFV).
  - Bond recovery measure: recovery of market value (RMV), denoted ψ (fraction of pre-default bond market value received upon default).
- Key mechanism and simplified relationships (under constant λ, flat risk-free rate, continuous premiums, neglecting accruals):
  - Fair CDS premium (simplified) ∝ λ(1−ω).
  - Bond risk premium (simplified) ∝ λ(1−ψ).
  - Equality of premiums (basis zero) holds only if recovery value is zero (0==ψω), or bond trades close to par (ψ ≈ ω).
  - When bond trades far below par, RFV ω is significantly lower than RMV ψ, producing a positive basis.
- Analogy: inconsistency akin to volatility smiles — an implied “recovery smile.”
- Numerical sensitivities (model example parameters and findings):
  - Risk-free term structure flat at 3 percent.
  - Underlying bonds: semiannual 9 percent-coupon, maturities of one, five, and ten years.
  - Bond par spreads considered: 500, 1,000, and 1,500 basis points.
  - For zero recovery the fair CDS spread equals intuitive value and basis is zero.
  - For higher ω the CDS spread becomes very sensitive to changes in ω.
  - Example implied default intensities for five-year CDS with given ω:
    - ω = 0.2 → implied intensity λ = 13.7 percent.
    - 5.0 = ω → implied intensity λ = 21.9 percent.
    - ω = 0.75 → implied intensity λ = 59.8 percent.
  - With high par spreads, higher ω increases implied default probability and can increase CDS spreads despite lower net costs to protection sellers upon default.
  - If protection buyers insure only current market price rather than full face amount, multiply fair CDS spread by market price — shifts curves but not curvature.
  - Allowing multiple deliverable bonds does not reverse the effect when underlying trades below par; existence of cheaper-than-underlying bonds increases the basis.

### IV. Empirical approach and application to sovereigns (methodological notes)
- Extraction of implied recovery values:
  - Risk-neutral recovery values can be approximated from bond prices (Merrick (2001); Andritzky (2005, 2006)) but require restrictive assumptions; sovereign soft restructurings may imply high recoveries correlated with bond price levels.
  - Combining historical CDS spreads with underlying bond prices in a no-arbitrage framework can reveal investors’ expected recovery value; empirical illustration provided for Brazil crisis of 2002–03.
- Empirical sample and contract selection:
  - Paper exclusively considers contracts with full restructuring to avoid contractual bias.
  - Notes on MR and MMR conventions (MR limiting delivery to bonds with maturity of 30 months or less after CDS maturity) are described.

### Brazil crisis of 2002–03 — empirical data analysis and stylized facts
- Episode selection criteria:
  - (i) prolonged period of spreads above 1,000 basis points;
  - (ii) rich CDS quote dataset;
  - (iii) existence of cash bonds with roughly comparable tenor to CDS;
  - (iv) CTD bonds trading below par.
- Trade and liquidity statistics:
  - Typical trade size: between $5 and $35 million, with a mean size of $7.5 million.
  - Brazil CDS mean bid-ask spread: 29.8 basis points (15 percent of respective mid-quote).
  - Brazil bond spreads: around 20 basis points.
  - During distress, CDS bid-ask spreads make up only around 3 percent of the CDS mid-quote.
- Term structure and co-movement:
  - Term structure inverted during distress: one-year CDS quoted higher than three- and five-year contracts until early 2003.
  - First-difference co-movement of CDS spreads: correlation coefficients amounting to 96 percent and 98 percent.
  - First principal component explains 98.6 percent of the variation (and 95.6 percent of the AR(1) residuals).
- Regression and explanatory factors:
  - VIX volatility index explains between 10 percent and 20 percent of variance in spread levels.
  - EMBI Global and term spread of U.S. Treasuries not meaningful determinants of CDS basis in this episode.
  - Most significant influence: underlying bonds trading below par:
    - Regression of basis on price difference to par explains more than 40 percent of variance.
    - If protection buyers buy only partial protection (insurance equal to current market price), the basis is positive solely in autumn 2002, reaching above 500 basis points.
  - Indicators of liquidity on CDS market contribute only marginally; literature suggests liquidity effects might widen basis by around five basis points for liquid bonds, and up to 50 or 75 basis points during distress according to some market traders.
- Conclusion from data: price effect of underlying bonds trading far below par is the main cause for CDS-cash bond spread discrepancy in the Brazil episode.

### Implied recovery values under a no-arbitrage framework (identification and findings)
- Method:
  - Assume observed CDS spread c_t = f_c(λ, ω) and dirty bond price P_t = f_P(λ, ω) under no-arbitrage.
  - Use one CDS spread and one corresponding bond price to solve for implied default intensity λ and implied recovery fraction of face ω (assumed constant over contract life).
- Mixed recovery model and identification:
  - No-arbitrage relationship involves three instruments: underlying bond, CTD bond, and CDS contract.
  - Unobservable variables: RMV fraction ψ, RFV fraction ω, intensity λ.
  - Model assumes constant hazard rate λ and a mixed recovery specification: total bond recovery value composed of RFV fraction ω and RMV fraction ψ multiplied by pre-default bond price.
  - Mixed recovery chosen because pure RFV estimation can exceed CTD price and break arbitrage; mixed recovery yields lower RFV-implied face recovery and adjusts λ downward.
- Empirical findings (Brazil data):
  - Implied recovery fraction of face ω extracted for different combinations of three- and five-year CDS and matching bonds.
  - Implied recovery rates during distress are much higher than the 25 percent RMV standard assumption.
  - Time series: implied recovery rates strongly correlate with overall bond price level (underlying cash bond price provides an upper bound for recovery value).
  - Translating implied recovery fraction of par into recovery fraction of bond market value ψ yields:
    - For five-year CDS: ψ between 0.74 and 0.80.
    - For three-year CDS: ψ close to 0.9.
- Detailed empirical summaries and statistics:
  - Correlation between implied recovery value and dirty price of CTD during crisis heights:
    - July 2002 to January 2003 correlation amounts to 85 percent for the three-year contract.
    - July 2002 to January 2003 correlation amounts to 83 percent for the five-year contract.
  - Level and composition:
    - For the five-year contract, RFV portion ω remains stable around 20 percent of face value while almost all variation originates from fluctuations in the ψ-recovery fraction.
    - During autumn 2002, when spreads peaked, implied total recovery value almost equals the CTD price — interpreted as markets expecting an imminent, but soft restructuring.
  - Calibration and numerical summaries:
    - CDS basis reached levels as high as 2,500 basis points during the crisis.
    - Implied recovery rate remained above 40 percent of par during most of the crisis.
    - Results show an almost constant recovery fraction of par of about 20 percent (ω), while RMV fraction ψ adds another portion of up to 25 percent to total implied recovery value.
  - Implication: CTD serves as a useful proxy for pricing CDS during crisis peaks.

### Theoretical implications and pricing mechanics
- Two mechanisms explaining why CDS spreads exceed bond spreads during distress beyond traditional basis effects:
  1. Overinsurance: At bond prices below par, a CDS insuring par value offers overinsurance, producing a positive basis.
  2. Delivery-choice effect: Relevant recovery rate for CDS is the post-default value of the CTD; a cheaper expected post-default CTD relative to the underlying increases the wedge between CDS and bond spreads.
- Simplified relationships:
  - Bond spread ≈ λ × (ψ−1) using RMV loss rate.
  - CDS spread ≈ λ × (ω−1) using RFV loss rate.
  - When bond price < par, an exogenously assumed recovery fraction of face value translates into a higher recovery fraction of market value; ω and ψ diverge and CDS spread increases nonlinearly with ω when bond price is below par.
- Practical inference: During crises, observed CDS and bond spreads can be used together (including CTD prices) to infer implied recovery parameters ω and ψ and default intensity λ.

### Conclusions (paper’s key takeaways)
- Recovery is not a relevant determinant of CDS spreads in nondistress periods, but when bonds trade considerably below par (distress), recovery plays a crucial role in CDS pricing and in functioning protection markets.
- The mixed recovery framework (ω and ψ) reconciles observed CDS-bond pricing during distress and clarifies the crucial role of the CTD.
- Empirical evidence from Brazil 2002–03 indicates markets expected a soft restructuring (high implied recovery relative to CTD) and that the CTD is a useful proxy for CDS pricing.

*Italic source: IMF Working Paper content unit (excerpts from _wp06254).*

### References..............................................................................................................

### _wp06254 - References

### I. Introduction — research questions and context
- CDS mechanics and credit events:
  - Protection buyer pays periodic premium until maturity or a predefined credit event.
  - Typical sovereign CDS contracts under ISDA allow restructuring as a credit event; triggers include (i) change in coupon rates, (ii) change in principal amount, (iii) postponement of interest or principal payment date, (iv) change in ranking of priority, (v) change in payment of interest or principal to a nonpermitted currency.
  - Physical delivery of the cheapest-to-deliver (CTD) bond occurs within 30 business days after a credit event.
- Key empirical observations motivating the study:
  - Distressed market trading and CTD squeezes can raise the actual recovery value relevant to protection buyers.
  - Soft restructurings in sovereign markets can imply actual recovery values as high as 60 percent, contrasting with analysts’ rule-of-thumb of using 25 percent to value CDS contracts under risk neutrality.
- Two research questions posed:
  - Whether the choice of recovery value affects CDS pricing when delta-hedging with cash bonds; in nondistressed (near-par) markets an overly low recovery assumption can be offset by underestimating implied default probability (Duffie (1999)), but this offset breaks down when bond prices trade far below par.
  - Whether information on expected recovery values can be extracted from CDS data to guide pricing in future distress situations; empirical extraction illustrated for the Brazil crisis of 2002–03.
- Observed relationships and implications:
  - For deeply distressed bonds: (i) bond-implied default intensity increases exponentially with the recovery fraction of par value, as do CDS spreads; (ii) CDS premiums (insurance on par) must exceed risk premia implied by bonds trading below par.
  - In soft restructurings, implied recovery values correlate closely with current distressed cash bond price levels; CDS-implied recovery rates can therefore be much higher than traditional assumptions.
- Literature context:
  - Key theoretical and empirical references cited: Duffie (1999); Hull and White (2000, 2001); Schönbucher (2004); Merrick (2001); Andritzky (2005, 2006); Pan and Singleton (2005); Zhang (2003); Packer and Suthiphongchai (2003); Longstaff, Mithal, and Neis (2005); Packer and Zhu (2005); Cossin, Hricko, Aunon-Nerin, and Huang (2002).

### II. CDS valuation framework and mathematical foundation
- Premium leg and protection leg definitions:
  - Buyer pays annual premium c per one unit of notional until maturity or a credit event; premium payments normally quarterly, at times t1,...,tN.
  - Premium leg present value (notation as in source): sum/integral expression shown as equation (1) using continuous risk-free rate tr and risk-neutral intensity tλ.
  - Protection leg present value integrates expected post-default payment: protection buyer receives difference between par and market value of eligible bond; accrued interest  and expected fractional recovery of face value ω̂ enter expressions.
  - Fair premium t c is chosen so premium leg equals protection leg at origination: equation (4).
- Specific modeling features preserved from source:
  - Default time τ, settlement time dτ within normally 30 business days so that d = 30,...,0 business days and d = 0,...,30 is referenced.
  - Recovery of face value (RFV) notation: ω(dτ) and accrued interest A(dτ); present-value-at-default forms ω̂ and Â.
  - Fractional accrued premium 4* c appears in payoffs at default (equation (2)).
- Important pricing implications emphasized:
  - CDS pricing depends critically on assumed recovery concept (RFV versus RMV) and on the relation between bond prices and implied default intensity.
  - When bonds trade far below par, the usual offset between assumed recovery and implied default probability fails, altering CDS spreads materially.

### III. The basis: reasons for CDS vs bond spread divergence
- Definition:
  - Basis = CDS spread − corresponding point on the term structure curve of bond spreads; positive basis when CDS premiums exceed bond spreads, negative basis otherwise.
- Conceptual and practical drivers of basis (as summarized from Table 1 and text):
  - Positive-basis drivers:
    - Delivery option: protection buyer can deliver any acceptable bond and receive par value.
    - Issuance of new bonds: pushes up demand for insurance, raising protection price.
    - Short selling abilities: CDS spreads can react faster to deteriorations as insurance demand increases.
    - Repo specialness: repurchase agreements on deliverable bonds can increase CDS spreads because such bonds are unavailable for delivery.
  - Negative-basis drivers:
    - Counterparty risk: premium compensates for protection seller default risk.
    - Bond illiquidity: illiquid paper often trades at higher spreads, reducing the basis (effect can be ambiguous).
    - Funding risk: protection seller does not incur funding risk that would arise if replicating the swap by buying the underlying funded at the risk-free rate.
- Empirical relevance and nuances:
  - Many basis effects are difficult to detect empirically; delivery option often small when a single CTD dominates.
  - In Argentina, Uruguay, and Brazil distress episodes, long-maturity or yen-denominated low-coupon issues often served as CTD.
  - Relative liquidity differences between cash and protection markets are significant drivers: Longstaff, Mithal, and Neis (2005) find liquidity proxies (bid-ask spread, principal amount) are most significant in explaining basis for 68 investment-grade corporations.
  - Contractual differences around restructuring clauses matter: Packer and Zhu (2005) find contracts allowing restructurings can have up to a 7 percent higher CDS spread compared with no-restructuring (NR) contracts; paper restricts empirical sample to contracts with full restructuring to avoid bias.
- Nontechnical mitigation channels:
  - Recovery swaps and post-delivery handling:
    - Protection seller receiving CTD might prefer not to hold distressed bonds for regulatory or liquidity reasons and can hedge exposure through recovery swaps (iTraxx or similar platforms).
    - Market participants providing recovery swaps include banks and dealers; netting and tear-ups (e.g., TriOptima) can reduce exposures and were used after events like Delphi’s bankruptcy.

### IV. Empirical approach and application to sovereigns (methodological notes)
- Extraction of implied recovery values:
  - Risk-neutral recovery values can be approximated from bond prices (Merrick (2001); Andritzky (2005, 2006)), but these require restrictive assumptions and typically find negative correlation between default likelihood and recovery value.
  - For sovereign soft restructurings, recovery does not necessarily imply NPV loss; observed close relation between implied recovery values and distressed bond price levels.
  - Combining historical CDS spreads with underlying bond prices in a no-arbitrage framework can reveal investors’ expected recovery value; empirical illustration provided for Brazil crisis of 2002–03.
- Empirical sample and contract selection:
  - To avoid contractual bias, the paper exclusively considers contracts with full restructuring.
  - Observations on market conventions: modified restructuring (MR) and modified-modified restructuring (MMR) terms are described, including MR limiting delivery to bonds with maturity of 30 months or less after CDS maturity.

*Source: _wp06254 - References (excerpts from the PDF content unit provided).*

### Box 2. Basis Effects from Nontechnical Factors—Some Recent Examples

### Box 2. Basis Effects from Nontechnical Factors—Some Recent Examples

### Nontechnical drivers of large CDS-bond basis
- Large basis during distress can arise from nontechnical factors such as:
  - a squeeze on certain bonds stemming from debt management (example: Brazil, August–September 2002 — squeeze on very short maturity, high-yield ‘04s and eligible interest (“EI”) bonds).
  - repo specialness (example: Argentina, around December 2001 — local banks closed short positions by repo-ing certain bonds at 15 percent, below the regulator’s 24 percent penalty, removing bonds from the market and leaving fewer deliverable bonds after the credit event).
- Central bank actions (example: the Brazilian central bank bought most of the Brazilian yen bonds) can further squeeze the market for CTD bonds and lead to higher CDS spreads; such intended actions (e.g., inexpensive buy-backs) may be misinterpreted and motivate sell-offs in the cash bond market.
- Other basis effects in high-grade debt markets are presumably small and difficult to gauge; focus here is on exceptional situations of major financial distress where these effects take a back seat.

### Evidence on the role of repo specialness and short-position closing
- Argentina anecdote: repo transactions at 15 percent removed bonds used as collateral from the market, reducing deliverable supply after a credit event.
- Such market mechanics can magnify the CDS basis by restricting deliverability.

---

### The role of recovery in CDS-bond basis
- Conceptual distinction:
  - CDS recovery measure: risk-neutral recovery of face value insured by the CDS contract, denoted ω (recovery of face value, RFV).
  - Bond recovery measure: recovery of market value (RMV), denoted ψ (fraction of pre-default bond market value received upon default).
- Key mechanism:
  - Duffie (1999) — varying default intensity and recovery fraction offset when pricing CDS per underlying bond market; offset works especially well for short maturities and low par spreads but fails in specific sovereign cases (low coupons, step-up language, long maturities, CTD trading far below par, long-maturity CDS contracts).
  - When bond and CDS markets assume different concepts of recovery and the CTD trades far below par, ω and ψ diverge and the offsetting mechanism fails, producing a large, positive basis during distress.
- Simplified formulas and implications (under constant default intensity λ, flat risk-free rate, continuous premium payments, neglecting accruals):
  - Fair CDS premium (simplified) ∝ λ(1−ω).
  - Bond risk premium (Duffie and Singleton 1999, simplified) ∝ λ(1−ψ).
  - Equality of premiums (basis zero) holds only if:
    - recovery value is zero (0==ψω), or
    - bond trades close to par (ψ ≈ ω).
  - When bond trades far below par, RFV recovery rate ω is significantly lower than RMV counterpart ψ, producing a positive basis.
- Analogy: inconsistency akin to volatility smiles in option markets — leads to an implied “recovery smile” (illustrated for Brazil, December 2004).
- Numerical sensitivities (model example parameters):
  - Risk-free term structure flat at 3 percent.
  - Underlying bonds: semiannual 9 percent-coupon, maturities of one, five, and ten years (same as CDS maturities modeled).
  - Bond par spreads considered: 500, 1,000, and 1,500 basis points.
  - Findings in example:
    - For zero recovery the fair CDS spread equals intuitive value and basis is zero.
    - For higher ω the CDS spread becomes very sensitive to changes in ω.
    - Example implied default intensities for five-year CDS with given ω:
      - ω = 0.2 → implied intensity λ = 13.7 percent.
      - 5.0 = ω → implied intensity λ = 21.9 percent. 
      - ω = 0.75 → implied intensity λ = 59.8 percent.
    - With high par spreads, higher ω increases implied default probability and can increase CDS spreads despite lower net costs to protection sellers upon default.
  - Note on partial protection: if protection buyers insure only current market price rather than full face amount, multiply fair CDS spread by market price — shifts curves in Figure 3 but not curvature; overall qualitative picture unchanged.
  - Allowing multiple deliverable bonds does not reverse the effect when underlying trades below par; existence of cheaper-than-underlying bonds increases the basis.

---

### Empirical data analysis (Brazil crisis of 2002–03)
- Selection criteria for episodes analyzed:
  - (i) prolonged period of spreads above 1,000 basis points;
  - (ii) rich CDS quote dataset;
  - (iii) existence of cash bonds with roughly comparable tenor to CDS;
  - (iv) CTD bonds trading below par.
- Brazil crisis of 2002–03 chosen as best match.
- Trade and liquidity statistics:
  - Typical trade size: between $5 and $35 million, with a mean size of $7.5 million.
  - Brazil CDS mean bid-ask spread: 29.8 basis points (15 percent of respective mid-quote).
  - Brazil bond spreads: around 20 basis points.
  - During distress, CDS bid-ask spreads make up only around 3 percent of the CDS mid-quote.
- Term structure and co-movement:
  - Term structure inverted during distress: one-year CDS quoted higher than three- and five-year contracts until early 2003.
  - First-difference co-movement of CDS spreads: correlation coefficients amounting to 96 percent and 98 percent.
  - First principal component explains 98.6 percent of the variation (and 95.6 percent of the AR(1) residuals).
- Regression and explanatory factors:
  - VIX volatility index explains between 10 percent and 20 percent of variance in spread levels.
  - Other measures (EMBI Global, term spread of U.S. Treasuries) not meaningful determinants of CDS basis.
  - Most significant influence: underlying bonds trading below par.
    - Regression of basis on price difference to par explains more than 40 percent of variance.
    - If protection buyers buy only partial protection (insurance equal to current market price), the basis is positive solely in autumn 2002, reaching above 500 basis points.
  - Indicators of liquidity on CDS market contribute only marginally to explaining the basis; literature suggests liquidity effects might widen basis by around five basis points for liquid bonds, and up to 50 or 75 basis points during distress according to some market traders.
- Conclusion from data analysis: the price effect of underlying bonds trading far below par is the main cause for discrepancy between CDS and cash bond spreads in the Brazil episode.

---

### Implied recovery values under a no-arbitrage framework
- Method:
  - Assume CDS priced under no-arbitrage; observed CDS spread c_t = f_c(λ, ω).
  - Dirty bond price P_t = f_P(λ, ω) under same no-arbitrage argument.
  - Use one CDS spread and one corresponding bond price to solve for implied default intensity λ and implied recovery fraction of face ω (assumed constant over contract life).
- Empirical findings (Brazil data):
  - Implied recovery fraction of face ω extracted for different combinations of three- and five-year CDS and matching bonds (Figures 6 and 7).
  - Implied parameters subsume statistical noise, residual basis effects, and maturity mismatches; they are risk-neutral measures and need not equal realized recovery values.
  - Striking result: implied recovery rate during distress is much higher than the 25 percent standard RMV assumption.
  - Time series behavior: implied recovery rates strongly correlate with overall bond price level (underlying cash bond price provides an upper bound for recovery value).
  - Translating implied recovery fraction of par into recovery fraction of bond market value ψ yields:
    - For five-year CDS: ψ between 0.74 and 0.80.
    - For three-year CDS: ψ close to 0.9.
- Implication: discrepancies between observed market CDS spreads and model-theoretic spreads may be explained largely by recovery-measure inconsistency when CTD bonds trade far below par; recovery effect is less pronounced at shorter maturities.

*Source: Box 2, “Basis Effects from Nontechnical Factors—Some Recent Examples,” from the provided IMF working paper content.*

### conclusion appears even more plausible for Brazil where the recovery rate implied from

### VI. IMPLIED RECOVERY VALUES UNDER NO ARBITRAGE WITH CTD

### Mixed recovery model and identification
- No-arbitrage relationship involves three instruments: the underlying bond, the cheapest-to-deliver (CTD) bond, and the CDS contract.
- Unobservable variables distinguished by the model:
  - RMV fraction, ψ
  - RFV fraction, ω
  - Intensity of a credit event, λ
- Model assumptions used for static estimation:
  - Constant hazard rate (constant λ) to enable identification of ω and ψ from daily prices of the three instruments.
  - Mixed recovery specification: total bond recovery value comprised of an RFV fraction (ω) and an RMV fraction (ψ) multiplied by the pre-default bond price.
- Rationale for mixed recovery:
  - Pure RFV implied from CDS and bond spreads can exceed the CTD's price and break the arbitrage relationship.
  - Mixed recovery yields lower recovery fraction of face value than implied by a naive RFV-only estimation and adjusts implied default intensity downward.
- Practical note: restructurings and maturity extension deals often resemble a mixed recovery framework where recovery value comprises two fractions, ω and ψ.

### Modeling choices and illustrative construction
- Constant default intensities justified because:
  - Introduction of face value recovery causes implied default intensity to level out in bootstrapping analysis.
  - Distressed bond prices show little sensitivity to long-term default intensity since survival probability in the distant future is very low.
  - CTD with much longer duration is only marginally affected by incorrect long-term default intensity.
- Figures 8 and 9 (illustrative) graph the recovery value of CDS split into RFV (ω) and RMV (ψ) components for three- and five-year contracts:
  - Graphed recovery value is discounted with the risk-free rate from the 75 percent quantile default time (point where cumulative default probability hits 75 percent).
  - ψ is multiplied with the current clean price of the CTD (does not account for fluctuations in expected pre-default price).
  - For three-year tenor the Brazil 2006 US$10.25 percent bond served as underlying; results for Brazil 2005 US$9.625 percent look comparable. For five-year tenor Brazil 2008 11.5 percent US$ bond served as underlying; other bonds look similar.

### Empirical findings from the Brazil 2002–03 crisis
- Two main empirical results from Figures 8 and 9:
  - The implied recovery value is found significantly higher than the 25 percent fraction of face most of the time.
  - Very high correlation between implied recovery value and the dirty price of the relevant CTD during the crisis heights:
    - Correlation from July 2002 to January 2003 amounts to 85 percent for the three-year contract.
    - Correlation from July 2002 to January 2003 amounts to 83 percent for the five-year contract.
- Level and composition of implied recovery rates:
  - For the five-year contract, the RFV portion, ω, remains stable around 20 percent of face value while almost all variation originates from fluctuations in the ψ-recovery fraction.
  - During autumn 2002, when spreads peaked, implied total recovery value almost equals the CTD price—interpreted as investor expectations about value recovered from a possible restructuring, suggesting markets expected an imminent, but soft restructuring.
- Calibration and numerical summaries:
  - CDS basis reached levels as high as 2,500 basis points during the crisis.
  - Implied recovery rate remained above 40 percent of par during most of the crisis (inferred from CDS and bond data).
  - Results show an almost constant recovery fraction of par of about 20 percent (ω), while the RMV fraction (ψ) adds another portion of up to 25 percent to the total implied recovery value.
  - Implied recovery value strongly correlated with the CTD during crisis peaks, supporting the CTD as a useful proxy for pricing CDS.

### Theoretical implications and pricing mechanics
- Two mechanisms explaining why CDS spreads exceed bond spreads during distress beyond traditional basis effects:
  1. Overinsurance: At bond prices below par, a CDS insuring par value offers overinsurance, producing a positive basis.
  2. Delivery-choice effect: The relevant recovery rate for CDS is the post-default value of the bond chosen for delivery (the CTD); a cheaper expected post-default CTD relative to the underlying increases the wedge between CDS and bond spreads.
- Simplified model relationships:
  - Bond spread ≈ λ × (ψ−1) using RMV loss rate.
  - CDS spread ≈ λ × (ω−1) using RFV loss rate.
  - When bond price < par, an exogenously assumed recovery fraction of face value translates into a higher recovery fraction of market value, and ωψ>.
  - Under risk-neutral consistent pricing, CDS spread increases nonlinearly (exponentially in model description) with higher ω when bond price is below par; this nonlinearity intensifies for higher spreads and longer CDS maturities.
- Practical inference: During crises, observed CDS and bond spreads can be used to infer implied recovery parameters, distinguishing ω and ψ by using prices of CDS, underlying bond, and CTD.

### Conclusions drawn in the paper
- Recovery is not a relevant determinant of CDS spreads in nondistress periods, but when bonds trade considerably below par (distress), recovery plays a crucial role in CDS pricing and in functioning protection markets.
- The mixed recovery framework (ω and ψ) reconciles observed CDS-bond pricing during distress and clarifies the crucial role of the CTD.
- Empirical evidence from Brazil 2002–03 indicates markets expected a soft restructuring (high implied recovery relative to CTD) and that the CTD is a useful proxy for CDS pricing.

*Italic source: IMF Working Paper content unit (excerpts from VI and VII).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06254.pdf_