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Credit Value Adjustment (CVA) is the difference between the value of the default-free and credit-risky derivative portfolio, which can be regarded as the cost of the credit hedge. Default probabilities are therefore needed, as input parameters to the valuation. When liquid CDS are available, then implied probabilities of default can be derived and used. However, in small markets, like the Nordic region of Europe, the…
In the third part of this series we introduce consistent relative value measures for CDS-Bond basis trades using the bond-implied CDS term structure derived from fitted survival rate curves. We explain why this measure is better than the traditionally used Z-spread or Libor OAS and offer simplified hedging and trading strategies which take advantage of the relative value across the entire range of maturities of cash …
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 present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral modeling, Gap Risk, Re-hypothecation, Wrong Way Risk, Basel III, inclusion of Funding costs, First t…
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 …
Recently, incomplete-market techniques have been used to develop a model applicable to credit default swaps (CDSs) with results obtained that are quite different from those obtained using the market-standard model. This article makes use of the new incomplete-market model to further study CDS hedging and extends the model so that it is capable treating single-name CDS portfolios. Also, a hedge called the vanilla hedg…
We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CDS premium rate formula, about the dynamics of liquidity rate processes and about the credit-liquidit…
In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this model using a chosen number of reference Credit Default Swap (CDS) market quotes. In general this model can be seen as a possible extension of the time-varying AT1P mo…
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…
Modern economic systems face unprecedented socioeconomic challenges, making systemic resilience and effective liquidity flow management essential. Traditional models such as CAPM, VaR, and GARCH often fail to reflect real market fluctuations and extreme events. This study develops and validates an innovative mathematical model based on the Navier-Stokes equations, aimed at the quantitative assessment, forecasting, an…
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…
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 …
We study two questions related to competition on the OTC CDS market using data collected as part of the EMIR regulation. First, we study the competition between central counterparties through collateral requirements. We present models that successfully estimate the initial margin requirements. However, our estimations are not precise enough to use them as input to a predictive model for CCP choice by counterparties i…
In this paper, we search whether the Benford's law is applicable to monitor daily changes in sovereign Credit Default Swaps (CDS) quotes, which are acknowledged to be complex systems of economic content. This test is of paramount importance since the CDS of a country proxy its health and probability to default, being associated to an insurance against the event of its default. We fit the Benford's law to the daily ch…
We study insolvency cascades in an interbank system when banks are allowed to insure their loans with credit default swaps (CDS) sold by other banks. We show that, by properly shifting financial exposures from one institution to another, a CDS market can be designed to rewire the network of interbank exposures in a way that makes it more resilient to insolvency cascades. A regulator can use information about the topo…
Bilateral CVA as currently implement has the counterintuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However, there are two significant omissions for practical implementation that come from the same source, i.e. positions not booked in us…
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.
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.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
PD is the probability a name defaults over a horizon — real-world for books, risk-neutral for CDS.
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.
CDS Basis Trade — Arbitrage between cash bonds and CDS contracts revealing funding and counterparty frictions.
Cheapest-to-deliver is the bond a futures (or CDS) seller will deliver because it minimizes their cost — the option that sits inside the contract.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
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.
CDS Basis Trade — Arbitrage between cash bonds and CDS contracts revealing funding and counterparty frictions.
Cheapest-to-deliver is the bond a futures (or CDS) seller will deliver because it minimizes their cost — the option that sits inside the contract.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
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.
PD is the probability a name defaults over a horizon — real-world for books, risk-neutral for CDS.