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This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on fa…
Using micro-level data, we construct a credit spread index with considerable predictive power for future economic activity. We decompose the credit spread into a component that captures firm-specific information on expected defaults and a residual component–– the excess bond premium. Shocks to the excess bond premium that are orthogonal to the current state of the economy lead to declines in economic activity and ass…
ABSTRACT Using dealer's quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly cross‐correlated, and principal components analysis implies they are mostly driven by a single common factor. Although …
ABSTRACT Most structural models of default preclude the firm from altering its capital structure. In practice, firms adjust outstanding debt levels in response to changes in firm value, thus generating mean‐reverting leverage ratios. We propose a structural model of default with stochastic interest rates that captures this mean reversion. Our model generates credit spreads that are larger for low‐leverage firms, and …
ABSTRACT This article examines the optimal capital structure of a firm that can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's (1994a) closed‐form results to a much richer class of possible debt structures and permit study of the optimal maturity of debt as …
Abstract Two intermediary-based factors—a corporate bond dealer inventory measure and a broad intermediary distress measure—explain more than 40$\%$ of the puzzling common variation in credit spread changes beyond canonical structural factors. A simple intermediary-based model with partial market segmentation accounts for intermediary factors’ explanatory power and delivers three further implications with empirical s…
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead …
In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula for constant maturity swaps in the default free swap market under the LIBOR market model. A "convexity adjustment"-like correction is present in the related formula…
We develop a structural credit-risk model under incomplete information in which investors observe firm value only indirectly through noisy market signals and scheduled corporate disclosures. While disclosure dates are known in advance, their informational content is random, leading to stochastic discontinuities in the observation process. We derive the Kushner-Stratonovich equation for structural credit-risk models w…
This paper develops a three-currency Heath-Jarrow-Morton framework in which corporate credit is treated as a separate economy, connected to the nominal and real economies through synthetic inflation and credit exchange rates. The framework produces a testable identity. Under joint no-arbitrage, the credit spread of an issuer expressed over the inflation-rateindexed risk-free curve equals the same issuer's credit spre…
ABSTRACT We model a loop between sovereign and bank credit risk. A distressed financial sector induces government bailouts, whose cost increases sovereign credit risk. Increased sovereign credit risk in turn weakens the financial sector by eroding the value of its government guarantees and bond holdings. Using credit default swap (CDS) rates on European sovereigns and banks, we show that bailouts triggered the rise o…
We study the nature of sovereign credit risk using an extensive sample of CDS spreads for 26 developed and emerging-market countries.Sovereign credit spreads are surprisingly highly correlated, with just three principal components accounting for more than 50 percent of their variation.Sovereign credit spreads are generally more related to the U.S. stock and high-yield bond markets, global risk premia, and capital flo…
Abstract We provide new empirical evidence that U.S. expected growth and consumption volatility are closely related to the strong comovement in sovereign spreads. We rationalize these findings in an equilibrium model with recursive utility for credit default swap (CDS) spreads. The framework links a reduced-form default process with country-specific sensitivity to expected growth and macroeconomic uncertainty. Exploi…
Current post-trade clearing systems rely almost exclusively on cash or cash-like collateral, leaving vast reserves of short-term liquidity embedded in trade credit outside formal settlement infrastructures. A key barrier to integrating this liquidity is the near-universal dependence of clearing services on novation, which imposes institutional overhead that restricts accessibility and limits the range of obligations …
A credit rating of AAA asserts near-certainty of repayment. This paper asks whether the pre-crisis information environment could have supported that assertion for structured products. Bayes' theorem implies that any reliability target requires a minimum level of statistical discrimination between instruments that will repay and those that will not. At structured-finance base rates, a four-nines reliability target dem…
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with empirical data. At the same time, it is desirable to still preserve some analytical tractability. We achieve both goals by putting forward an ensemble approach for the asset correlations.…
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio …
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures (standard deviation, VaR and Expected Shortfall) as well as allocation of risk down to individual transactions. The underlying model is the industry standard multi-factor Merton-type mod…
Bank CDS Index tracks the cost of insuring major bank credit risk and serves as a real-time indicator of banking-system stress and confidence.
Fractional-reserve banking is taking deposits and holding only a fraction in reserves or liquid assets — credit creation with a run risk.
KBW Bank Index tracks the equity performance of major U.S. banks and provides insight into banking-sector health, credit transmission, and market confidence.
Regional Bank ETF performance helps track stress in smaller and mid-sized banks, especially around deposit stability, asset quality, and local credit conditions.
An ABS is a bond paid from a pool of receivables — cards, auto, equipment — sliced into tranches with a waterfall.
Bankruptcy is a court process that stays creditors and restructures or liquidates claims when a firm cannot meet its obligations as they come due.
CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.
CDX IG Index tracks the cost of insuring a basket of North American investment-grade corporate credit and is widely used as a real-time gauge of credit stress and financial conditions.
Chapter 11 is US reorganization bankruptcy — the firm tries to stay a going concern while claims are rewritten.
Chapter 7 is US liquidation bankruptcy — a trustee sells assets and pays claims in priority; the going concern is over.
A CDO is a securitization of debt (or of other securitizations) into tranches — correlation and a waterfall, not a simple bond.
A convertible is a bond plus an embedded call on the issuer’s stock — credit with equity convexity, or equity with a coupon, depending on the delta.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
A credit rating is an agency’s opinion of relative default risk — a letter grade that gates mandates, not a market price.
Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.
A debt covenant is a contractual limit on the borrower — maintain a ratio, not do a thing, or report a thing — that turns a miss into a default or a fee.
Default risk is the chance the issuer misses a contractual payment — the event credit spread is trying, noisily, to price.
Funding Valuation Adjustment — Funding cost adjustment in uncollateralized derivative books.
High Yield OAS measures the spread of high-yield corporate bonds over risk-free Treasuries after adjusting for embedded options, serving as a key gauge of speculative credit stress.
Interest coverage is EBIT (or EBITDA) divided by interest expense — how many times operating profit can pay the coupon bill.
Investment grade is a credit rating of BBB− / Baa3 or better — a regulatory and mandate bucket, not a promise of no loss.
Investment Grade OAS measures the spread of high-quality corporate bonds over Treasuries after adjusting for embedded options, helping track broad corporate credit conditions.
A junk bond is a high-yield, below-investment-grade credit — more equity-like default risk, still quoted in spread and price.
A leveraged buyout is a purchase financed mostly with debt on the target’s cash flows — private equity’s standard carry trade on coverage.
The Loan Officer Survey tracks bank lending standards and loan demand, providing insight into whether credit supply is tightening or easing in the real economy.
LGD is 1 minus recovery — the fraction of exposure lost when default happens.
PD is the probability a name defaults over a horizon — real-world for books, risk-neutral for CDS.
Recovery is what a claim is worth after default, as a fraction of par — the complement of loss given default.
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
Risk-on / risk-off (RORO) is a one-factor tape: the same risk appetite impulse hits credit, EM, high-beta equity, and vol in one direction while Treasuries, the dollar, and gold take the other side.
TINA — There Is No Alternative — was the 2010s slogan that zero rates left no choice but equities (or credit), compressing risk premia because cash paid nothing.
Wrong-way risk is when exposure rises at the same time the counterparty’s credit worsens — the hedge or the receivable fails exactly when you need it.
China credit impulse measures the change in new credit growth relative to GDP and is widely used as a leading indicator for Chinese demand and global cyclical momentum.
EMBI sovereign spread measures the yield premium on emerging-market sovereign debt over U.S. Treasuries and serves as a key gauge of EM credit risk and external financing stress.
Amortization is the write-down of an intangible (or the scheduled paydown of a loan) — two different words sharing a calendar.
Private Equity Dry Powder — Undeployed PE capital that can support LBO activity and credit demand.
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
An ABS is a bond paid from a pool of receivables — cards, auto, equipment — sliced into tranches with a waterfall.
Bank CDS Index tracks the cost of insuring major bank credit risk and serves as a real-time indicator of banking-system stress and confidence.
Bankruptcy is a court process that stays creditors and restructures or liquidates claims when a firm cannot meet its obligations as they come due.
CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.
CDX IG Index tracks the cost of insuring a basket of North American investment-grade corporate credit and is widely used as a real-time gauge of credit stress and financial conditions.
Chapter 11 is US reorganization bankruptcy — the firm tries to stay a going concern while claims are rewritten.
Chapter 7 is US liquidation bankruptcy — a trustee sells assets and pays claims in priority; the going concern is over.
China credit impulse measures the change in new credit growth relative to GDP and is widely used as a leading indicator for Chinese demand and global cyclical momentum.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
A CDO is a securitization of debt (or of other securitizations) into tranches — correlation and a waterfall, not a simple bond.
Commercial Mortgage Delinquency — Office and retail stress feeding through CRE credit and regional bank risk.
Long the convertible and short the delta in the stock — harvest cheap implied vol / credit, with funding and squeeze risk.
A convertible is a bond plus an embedded call on the issuer’s stock — credit with equity convexity, or equity with a coupon, depending on the delta.
Copula Models — Dependence modeling linking marginal distributions — infamous from 2008 structured credit.
Countercyclical Capital Buffer — Bank capital requirements that tighten or ease through the credit cycle.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
A credit rating is an agency’s opinion of relative default risk — a letter grade that gates mandates, not a market price.
Credit Suisse’s March 2023 state-brokered sale to UBS wrote AT1s to zero while common equity kept residual value — a hierarchy shock that repriced the entire AT1 market.
Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
A debt covenant is a contractual limit on the borrower — maintain a ratio, not do a thing, or report a thing — that turns a miss into a default or a fee.
Default risk is the chance the issuer misses a contractual payment — the event credit spread is trying, noisily, to price.