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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 …
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollov…
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…
Persistent shifts in term-structure dynamics undermine the stability of single-regime models in long samples. We develop an arbitrage-free regime-switching generalized CIR (RS-GCIR) model that jointly prices the Chinese government bond (CGB) curve and corporate bond curves. To capture the systematic transmission from interest-rate conditions to credit spreads, we structure the model into two blocks and price corporat…
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 …
We consider an equity market subject to risk from both unhedgeable shocks and default. The novelty of our work is that to partially offset default risk, investors may dynamically trade in a credit default swap (CDS) market. Assuming investment opportunities are driven by functions of an underlying diffusive factor process, we identify the certainty equivalent for a constant absolute risk aversion investor with a semi…
This paper presents the experimental process and results of SVM, Gradient Boosting, and an Attention-GRU Hybrid model in predicting the Implied Volatility of rolled-over five-year spread contracts of credit default swaps (CDS) on European corporate debt during the quarter following mid-May '24, as represented by the iTraxx/Cboe Europe Main 1-Month Volatility Index (BP Volatility). The analysis employs a feature matri…
We compare the five major sources of corporate Credit Default Swap prices: GFI, Fenics, Reuters, CMA, and Markit, using the most liquid single name 5-year CDS in the iTraxx and CDX indexes from 2004 to 2010. Deviations from the common trend among prices in the different databases are not random but are explained by idiosyncratic factors, financing costs, global risk, and other trading factors. The CMA quotes lead the…
The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than attempting to fit spreads -- and as we discuss here, the Z-spread is unsuitable -- we fit parametrised survival curves. By deriving a valuation formula for a risky bond, we explain and …
Risk-neutral default probabilities can be implied from credit default swap (CDS) market quotes. In practice, mid CDS quotes are used as inputs, as their risk-neutral counterparts are not observable. We show how to imply risk-neutral default probabilities from bid and ask quotes directly by means of formulating the CDS calibration problem to bid and ask market quotes within the conic finance framework. Assuming the ri…
One of the most challenging aspects in the analysis and modelling of financial markets, including Credit Default Swap (CDS) markets, is the presence of an emergent, intermediate level of structure standing in between the microscopic dynamics of individual financial entities and the macroscopic dynamics of the market as a whole. This elusive, mesoscopic level of organisation is often sought for via factor models that …
Fixed income has received far less attention than equity portfolio optimisation since Markowitz' original work of 1952, partly as a result of the need to model rates and credit risk. We argue that the shape of the efficient frontier is mainly controlled by linear constraints, with the standard deviation relatively unimportant, and propose a two-factor model for its time evolution.
In order to scale transaction rates for deployment across the global web, many cryptocurrencies have deployed so-called "Layer-2" networks of private payment channels. An idealized payment network behaves like a Credit Network, a model for transactions across a network of bilateral trust relationships. Credit Networks capture many aspects of traditional currencies as well as new virtual currencies and payment mechani…
This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in fav…