Credit Events Research Articles

Valuation of Credit Contingent Options with Applications to Quanto CDS

We study the valuation of credit-contingent asset or options by modelling the correlation between asset price and credit default. We provide three ways of modelling such correlation: (1) asset value follows a diffusion process with a one-time jump (such as currency devaluation) at the time of credit default; (2) Default intensity and asset price are driven by correlated Brownian motions in addition to the jump; (3) Default time and future asset price are correlated through a copula. When both asset price and credit default are independent of interest rates, such contract can be valued on a two-dimensional lattice (or finite-difference grid) in the second approach. We show that for a large class of one-factor default rate models, the computation can be reduced to one-dimension, a property often reserved for the affine class of models. We also obtain analytical solutions if default hazard rate, asset price return, and the copula are all Gaussian. Our experience shows that valuation is much more sensitive to the first and third type of correlations. We apply the model to the valuation of extinguishable FX swaps that terminate upon a credit event and quanto credit default swaps where premium and protection legs are paid in different currencies.

Modelling Short-Term Interest Rate Spreads in the Euro Money Market

In the framework of a new money market econometric model, we assess the degree of precision achieved by the European Central Bank ECB) in meeting its operational target for the short-term interest rate and the impact of the U.S. sub-prime credit crisis on the euro money market during the second half of 2007. This is done in two steps. Firstly, the long-term behaviour of interest rates with one-week maturity is investigated by testing for co-breaking and for homogeneity of spreads against the minimum bid rate (MBR, the key policy rate). These tests capture the idea that successful steering of very short-term interest rates is inconsistent with the existence of more than one common trend driving the one-week interest rates and/or with non-stationarity of the spreads among interest rates of the same maturity (or measured against the MBR). Secondly, the impact of several shocks to the spreads (e.g. interest rate expectations, volumes of open market operations, interest rate volatility, policy interventions, and credit risk) is assessed by jointly modelling their behaviour. We show that, after August 2007, euro area commercial banks started paying a premium to participate in the ECB liquidity auctions. This puzzling phenomenon can be understood by the interplay between, on the one hand, adverse selection in the interbank market and, on the other hand, the broad range of collateral accepted by the ECB. We also show that after August 2007, the ECB steered the risk-free rate close to the policy rate, but has not fully off-set the impact of the credit events on other money market rates. JEL Classification: C32, E43, E50, E58, G15

Robust Recovery Risk Hedging: Only the First Moment Matters

Credit derivatives are subject to at least two sources of risk: the default time and the recovery payment. This paper examines the impact of modeling the recovery payment on hedging strategies in a reduced-form model as well as a structural model. We show that all hedging approaches based on a quadratic criterion do only depend on the expected recovery payment at default and not the whole shape of the recovery payment distribution if the underlying hedging instrument (say, a defaultable zero coupon bond) jumps to or reaches a pre-specified value when the credit event occurs. This justifies assuming a \emph{certain} recovery rate conditional on default time and interest rate level. Hence, this result allows a simplified modeling of credit risk.

An Efficient Algorithm for Basket Default Swap Valuation

Monte Carlo simulation has become a workhorse of practical derivatives valuation because it is often impossible to construct theoretical pricing models for real world instruments in closed form. Credit derivatives are a case in point. But a major problem in the use of simulation methods for securities tied to default risk is that they are often written on baskets of individual credits, meaning that the number of correlated random variables to simulate can be very large, and the derivative9s value depends heavily on the correlations among defaults. Individual defaults are very low probability events, so joint defaults are rare indeed. Often, a great many Monte Carlo paths must be simulated to produce even a single credit event for a contract like a k-th-to-default basket swap. Importance sampling, which focuses the simulation effort on the most important paths for a given problem, is a useful variance reduction technique. In this article, the authors present an importance sampling methodology that is easy to implement and guarantees variance reduction for k-th-to-default basket swaps. A set of numerical examples using 1st-, 2nd- and 3rd-to-default contracts based on industry portfolios, each containing five bonds, demonstrates how powerful the approach is. The amount of variance reduction depends on the level of correlation among the credits, which is substantial, and can be an order of magnitude, or even more, for highly correlated risks. <b>TOPICS:</b>Credit default swaps, simulations, technical analysis

Portfolio Credit Risk

In order to take advantage of credit portfolio management opportunities, management must first answer several technical questions: What is the risk of a given portfolio? How do different macroeconomic scenarios, at both the regional and the industry sector level, affect the portfolio's risk profile? What is the effect of changing the portfolio mix? How might risk-based pricing at the individual contract and the portfolio level be influenced by the level of expected losses and credit risk capital? This paper describes a new and intuitive method for answering these technical questions by tabulating the exact loss distribution arising from correlated credit events for any arbitrary portfolio of counterparty exposures, down to the individual contract level, with the losses measured on a marked-to-market basis that explicitly recognizes the potential impact of defaults and credit migrations.

A Primer on Constant Proportion Debt Obligations

A Constant Proportion Debt Obligation (CPDO) is best described as an investment strategy rather than an asset class. It is a debt-issuing special-purpose vehicle that employs the majority of cash received from note holders in a cash reserve account of liquid, high-quality assets and a small amount to pay initial deal expenses and then makes a leveraged synthetic investment in an index of debt securities. The example cited in this article involves selling protection on the iTraxx and CDX credit default swap indices, rolling from an off-the-run index into a new on-the run index every six months. The article describes the workings of CPDOs by explaining their initial flows, their revenue and expense items, and their three operating rules, which cover investment, cash in and cash out, and leverage. The authors explain the three risks CPDOs face: credit events on the portfolio they have sold protection on, a loss in exiting the old off-the-run index, and a low premium on the new on-the-run index. They further break down the cost of exiting the old index into an increase in the mid-market level of the index and an increase in the bid-ask spread of the index. The authors provide a brief discussion of interest rate risk, path dependency, and risk correlation in CPDOs. They conclude the article by showing the resiliency of one particular CPDO structure via scenario analysis. Their analysis demonstrates that, in keeping with its AAA ratings, it takes extreme conditions to cause a loss in this particular CPDO deal. <b>TOPICS:</b>Credit risk management, credit default swaps

Reduced Form Modelling for Credit Risk

The purpose of this paper is to present in a unified context the reduced form modelling approach, in which a credit event is modelled as a totally inaccessible stopping time. Once the general framework is introduced (frequently referred to as pure intensity set-up), we focus on the special case where the full information at the disposal of the traders may be split in two sub-filtrations, one of them carrying the information of the occurrence of the credit event (in general referred to as hazard process approach). The general pricing rule when only one filtration is considered reveals to be non tractable in most of cases, whereas the second construction leads to much simplest formulas. Examples are given and evidence advanced that this set-up is more tractable.

Simple Computational Methods For Pricing Equity Default Swaps

ABSTRACT. An Equity Default Swap (EDS) is a hybrid credit-equity instrument which pays out a fixed sum upon the occurrence of an adverse equity or credit event. We describe two pricing methods and their associated accelerated simulation pricing engines. We find that when used in combination the engines result in a highly accurate and accelerated pricing system. This along with the system's inherent flexibility allows for the real-time pricing of the EDS. Therefore the system meets the needs of even the most demanding practitioners.

Good and bad credit contagion: Evidence from credit default swaps

This study examines the intra-industry information transfer effect of credit events, as captured in the credit default swaps (CDS) and stock markets. Positive correlations across CDS spreads imply that contagion effects dominate, whereas negative correlations indicate competition effects. We find strong evidence of contagion effects for Chapter 11 bankruptcies and competition effects for Chapter 7 bankruptcies. We also introduce a purely unanticipated event, in the form of a large jump in a company's CDS spread, and find that this leads to the strongest evidence of credit contagion across the industry. These results have important implications for the construction of portfolios with credit-sensitive instruments.

Pricing Credit Default Swaps when Interest Rate Process and Hazard Rate Process are Stochastic

This paper models the dynamics of the building blocks for a plain vanilla credit default swap. We use a normal process for the interest rate (Vasicek model) to model the price of zero-coupon bonds (or the discount factor) and a log-normal process for the hazard rate to model the survival probabilities in a java applet. Model-generated data are used to calculate a fair market price for such a contract once survival probabilities and values of the discount function have been estimated using stochastic models. The article concludes by presenting numerical results from the models. Combining a constant interest rate and a stochastic hazard rate process, this one-factor model shows that the level of hazard rate rather than the volatility affecting the change in CDS spreads the most. With a constant survival probability and a stochastic interest rate, a lower CDS spread is associated with a higher spot rate due to the protection buyer's higher opportunity cost on the premium payments. Results also show that a higher survival probability of the reference entity indicates a lower CDS spread as expected. A two-factor model gives a much higher CDS price than the one-factor model especially when the drift parameters are higher in the credit events process.

Credit-Linked Notes

A credit linked note (CLN) is a type of funded credit derivative in which the investor in the note, the credit protection seller, makes an upfront payment to the issuer of the note, the protection buyer. If no credit event occurs during the life of the note, the redemption value of the note is paid to the investor upon maturity. If a credit event does occur, then a value less than par is paid out to the investor upon maturity. For the investor, a CLN may entail some additional credit risk in return for a coupon that is somewhat higher than for other comparable investments in the market. This article explains how CLNs work and discusses some recent applications. <b>TOPICS:</b>Credit default swaps, credit risk management

Forecasting credit event frequency – empirical evidence for West German firms

The main challenge of forecasting credit default risk in loan portfolios may be seen in forecasting the default probabilities and the default correlations. We derive a Merton-style threshold value model for the default probability which treats the asset value of a firm as unknown and uses a factor model instead. In addition, we demonstrate how default correlations can be easily modeled. The empirical analysis is based on a large data set of German firms provided by Deutsche Bundesbank. We find that default probabilities can be forecast given the values of risk drivers known at the point of time at which the forecast is made. In addition, correlations depend on the fit of the estimated default probabilities to the realized default rate for given points in time.

Default Risk Premia and Asset Returns

This paper investigates the source for common variation in the portion of returns observed in U.S. credit markets that is not related to changes in risk-free rates or expected default losses. We extract a latent common component from firm-specific changes in default risk premia that is orthogonal to known systematic risk factors during our sample period from 2001 to 2004. Asset pricing tests using returns on Bloomberg-NASD corporate bond indices suggest that our discovered latent changes in default risk premia (DRP) factor is priced in the corporate bond market. A cross-sectional analysis of Merrill Lynch corporate bond portfolios sorted on either industry, maturity or rating supports these findings. In our tests we control for firm characteristics and find that the common variation in changes in default risk premia is not likely to be due to these. Using portfolios of put options written on the S&P 500 index and sorted on moneyness and maturity, we find that, for far-out-of-the-money options, both average returns and the beta estimate for our DRP factor increase with increasing time to maturity. The same holds true for out-of-the-money and at-the-money index put options. There is little to no evidence, however, of the DRP factor being priced in the equity markets. We develop a theoretical framework that, while the DRP factor is part of the pricing kernel, supports our empirical findings. It shows that the DRP factor captures the jump-to-default risk associated with market-wide credit events.

A simple probabilistic approach to the pricing of credit default swap covenants

In its original credit derivatives definitions, the International Swaps and Derivatives Association set out six credit events that can trigger payment on a default swap and many other obligation and settlement clauses that potentially affect the value of a credit default swap. Market participants have since attempted to reduce the list of events that could trigger payouts by eliminating so-called 'soft' credit events. Such events are indeed more akin to credit deterioration than default. In many instances, financial institutions are now left with mismatching contract clauses leading to potential basis risks in their books (contracts traded before and after changes in market practices but also contracts containing deliberate changes to standard clauses). The purpose of this analysis is to provide a few simple rules for calculating more precisely the impact of the different contract provisions on the price of a default swap.

Intra-Industry Credit Contagion: Evidence from the Credit Default Swap and Stock Markets

This study examines the information transfer effect of credit events across the industry, as captured in the Credit Default Swaps (CDS) and stock markets. Positive correlations across CDS spreads imply dominant contagion effects, whereas negative correlations indicate competition effects. We find strong evidence of dominant contagion effects for Chapter 11 bankruptcies and competition effect for Chapter 7 bankruptcies. We also introduce a purely unanticipated event, which is a large jump in a company's CDS spread, and find that this leads to the strongest evidence of credit contagion across the industry. These results have important implications for the construction of portfolios with credit-sensitive instruments.

Modeling the Effect of Macroeconomic Factors on Corporate Default and Credit Rating Transitions

In the reduced-form approach to credit modeling, default frequency has been found to depend on several firm-specific factors, most notably credit rating. But aggregate default rates also vary substantially over time, presumably reflecting changes in general economic conditions. In this paper, we fit Cox intensity models for major credit events, including defaults as well as major upgrades and downgrades in credit rating. The sample covers all corporate issuers in Moody's corporate bond Default Research Database over the period 1981-2002. The models incorporate both firm-specific factors related to a firm's credit rating history and a broad range of macroeconomic variables. Our results show that intensities of occurrence of credit events are significantly influenced by macro factors.

The Pricing of Credit Default Swaps During Distress

Credit default swaps (CDS) provide the buyer with insurance against certain types of credit events by entitling him to exchange any of the bonds permitted as deliverable against their par value. Unlike bonds, whose risk spreads are assumed to be the product of default risk and loss rate, CDS are par instruments, and their spreads reflect the partial recovery of the delivered bond's face value. This paper addresses the implications of the difference between bond and CDS spreads and shows the extent to which the recovery assumption matters for determining CDS spreads. A no-arbitrage argument is applied to extract recovery rates from CDS and bond markets, using data from Brazil's distress in 2002-03. Results are related to the observation that preemptive restructurings are now more common than straight defaults in sovereign bond markets and that this leads to a decoupling of CDS and bond spreads.

The Pricing of Credit Default Swaps During Distress

Credit default swaps (CDS) provide the buyer with insurance against certain types of credit events by entitling him to exchange any of the bonds permitted as deliverable against their par value. Unlike bonds, whose risk spreads are assumed to be the product of default risk and loss rate, CDS are par instruments, and their spreads reflect the partial recovery of the delivered bond's face value. This paper addresses the implications of the difference between bond and CDS spreads and shows the extent to which the recovery assumption matters for determining CDS spreads. A no-arbitrage argument is applied to extract recovery rates from CDS and bond markets, using data from Brazil's distress in 2002-03. Results are related to the observation that preemptive restructurings are now more common than straight defaults in sovereign bond markets and that this leads to a decoupling of CDS and bond spreads.

Innovations in Mortgage Modeling: An Introduction

∗This special issue presents a selection of recent methodological advances in the academic literature on mortgage performance and valuation. The articles include a range of modeling techniques from rational structural models applied to pool-level data and loan-level reduced-form, or behavioral, models of prepayment and default. Both classes of model are shown to be effective for evaluating innovations in contracting such as defeasance options in commercial mortgage contracts and hybrid residential mortgage products. Finally, the articles highlight a number of important methodological linkages between recent advances in mortgage modeling and those found in the valuation of other forms of risky debt such as corporate bonds. The structural models presented here focus on pricing and modeling credit or call events that are specific to a particular class of borrower. These models focus on the underlying dynamics of interest rates and the assets that are the collateral on the mortgage. Credit (or call) events are triggered by random movements in the asset price relative to a threshold that is the exercise price on the option. By modeling credit or call events in terms of the underlying dynamics of asset prices and/or interest rates, the structural methodology functionally links option exercise events to the underlying fundamentals faced by the borrower. These articles build upon an extensive literature with a corporate debt focus: Leland (1994), Jarrow and Turnbull (1995), Longstaff and Schwartz (1995), Leland and Toft (1996), Anderson and Sundaresan (2000), Collin-Dufresne and Goldstein (2001) and Huang and Huang (2002), among many others. They also build upon important prior structural mortgage models including Dunn and McConnell (1981a,b), Timmis (1985), Johnston and van Drunen (1988), Kau et al. (1992), Stanton (1995), Kau et al. (1995) and Kau and Slawson (2002), among many others. In contrast, reduced-form, or behavioral, approaches, do not explicitly model the value of the borrower’s assets and capital structure. Instead credit and/or

Catching Fallen Angels (and Other Expensive Credit Events)

We examine the efficacy of the I-squared incomplete information credit model in a broad context that is relevant to fund and asset managers. Using a rigorous statistical analysis, we show that I-squared is a powerful forecaster of the following events: - Rating agency downgrades - Investment grade to high yield downgrades - High yield defaults These statistical results translate directly into useful portfolio construction techniques. For example, we show that the number of high-yield defaults in a portfolio can be reduced dramatically by excluding a very small number of names.