Credit Spread Research Papers - Academia.edu (original) (raw)

Structural models for pricing credit risk can be used to forecast the spread on risky bonds and for hedging credit risk. This article examines the forecasting accuracy of the Black -Scholes -Merton (BSM) model of risky debt using a data set consisting of weekly bond data for First Interstate Bancorp over the period January 1986-August 1993. In addition, structural model hedge parameters and credit spread options are tested for their effectiveness in hedging the increasing credit risk premium on First Interstate Bancorp debt. Credit spread options in combination with a duration hedge offer the best hedging strategy, reducing the standard deviation of the hedging error by a minimum of 84%. D

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- Law, Risk Management, Financial Analysis, Standard Deviation

In Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. The valuation model of inflation-indexed (or equivalently foreign-currency) convertible bonds derived in this paper considers two sources of uncertainty allowing both the underlying stock and the consumer-price-index to be stochastic and incorporates credit risk in the analysis. We approximate the pricing equations by using a Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate the sensitivity of the theoretical values with respect to the characteristics of the issuer, the economic environment and the security s characteristics (number of principal payments). Moreover, we demonstrate the usefulness and the limitations of the pricing model by using inflation-indexed and foreign-currency linked convertibles traded on the Tel- Aviv stock exchange.

- by Alon Raviv
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- Business, Inflation, Credit Spread, Exchange rate
- by Haluk Unal
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- Capital Structure, Model Calibration, Credit Spread, Interest Rate

We model and examine the financial aspects of the land development process incorporating the industry practice of preselling lots to builders through the use of option contracts as a risk management technique. Using contingent claims valuation, we are able to determine endogenously the land value, presale option value, credits spreads and the effects of presales on debt pricing and equity expected returns. We show that using presales options effectively shift market risk from the land developer to the builder. Results from the model are consistent with the high rates of return on equity observed in empirical surveys; they also suggest that developers may be justified in pursuing projects with substantially lower expected returns to equity when a large number of lots can be presold. Additionally, we show that presales reduce default risk dramatically for leveraged projects and can support a considerable reduction in the cost of construction financing. Large debt risk premiums are justified for highly levered projects, which helps explain the use of mezzanine financing in the land development industry to reduce expected default costs.

- by Steven Ott
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- Risk Management, Applied Economics, Land Development, Rate of return

We discuss extensions of reduced-form and structural models for pricing credit risky securities to portfolio simulation and valuation. Stochasticity in interest rates and credit spreads is captured via reduced-form models and is incorporated with a default and migration model based on the structural credit risk modelling approach. Calculated prices are consistent with observed prices and the term structure of default-free and defaultable interest rates. Three applications are discussed: (i) study of the inter-temporal price sensitivity of credit bonds and the sensitivity of future portfolio valuation with respect to changes in interest rates, default probabilities, recovery rates and rating migration, (ii) study of the structure of credit risk by investigating the impact of disparate risk factors on portfolio risk, and (iii) tracking of corporate bond indices via simulation and optimisation models. In particular, we study the effect of uncertainty in credit spreads and interest rates on the overall risk of a credit portfolio, a topic that has been recently discussed by Kiesel et al. [The structure of credit risk: spread volatility and ratings transitions. Technical report, Bank of England, ISSN 1268ISSN -5562, 2001], but has been otherwise mostly neglected. We find that spread risk and interest rate risk are important factors that do not diversify away in a large portfolio context, especially when high-quality instruments are considered.

- by Stavros A. Zenios
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- Production Management, Multidisciplinary, Credit Risk, Default Risk

This work empirically examines six structural models of the term structure of credit risk spreads: Merton (1974), Longstaff & Schwartz (1995) (with and without stochastic interest rates), Leland & Toft (1996), Collin-Dufresne & Goldstein (2001), and a constant elasticity of variance model. The conventional approach to testing structural models has involved the use of observable data to proxy the latent capital structure process, which may introduce additional specification error. This study extends Jones, Mason & Rosenfeld (1983) and Eom, Helwege & Huang (2004) by using implicit estimation of key model parameters resulting in an improved level of model fit. Unlike prior studies, the models are fitted from the observed dynamic term structure of firm-specific credit spreads, thereby providing a pure test of model specification. The models are implemented by adapting the method of Duffee (1999) to structural credit models, thereby treating the capital structure process is truly latent,...

- by Iain C Maclachlan
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- Time Series, Capital Structure, Parameter estimation, Kalman Filter

This paper models the default probabilities and credit spreads for select Indian firms in the Black-Scholes-Merton framework. Counter to previous research, we show that the objective (or 'real') probability estimates are higher than the risk-neutral estimates over the sample period. However, the probability measure is found to be robust to the 'default trigger point'. The model output also compares favorably with the default rate reported by CRISIL's Average 1-year rating transitions as well as the Altman Z-score measure.

- by Alok Kumar Mishra
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- Credit Spreads, Credit Risk, Credit Spread, Probability of Default

Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection ('grace') period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer's optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.

- by Svein-Arne Persson
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- Modeling, Multidisciplinary, Financial Institutions, Capital
- by Monique Jeanblanc
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- Credit Rating, Credit Risk, Case Study, Credit Spread
- by Christian Hipp
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- Credit Rating, Credit Risk, Case Study, Credit Spread

We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by in the following way: (i) it incorporates informational noise in continuous time, (ii) it respects the (H) hypothesis, (iii) it precludes arbitrage from insiders. The model is sufficiently general to encompass a large class of structural models. In this setting we show that the default time is totally inaccessible in the market's filtration and derive the martingale hazard process. Finally, we provide pricing formulas for default-sensitive claims and illustrate with particular examples the shapes of the credit spreads and the conditional default probabilities. An important feature of the conditional default probabilities is they are non Markovian. This might shed some light on observed phenomena such as the "rating momentum".

- by Hélyette Geman and +1
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- Applied Mathematics, Statistics, Default Risk, Credit Spread

We measure dynamic risk exposure of hedge funds to various risk factors during different market volatility conditions using the regime-switching beta model. We find that in the high-volatility regime (when the market is rolling-down) most of the strategies are negatively and significantly exposed to the Large-Small and Credit Spread risk factors. This suggests that liquidity risk and credit risk are potentially common factors for different hedge fund strategies in the down-state of the market, when volatility is high and returns are very low. We further explore the possibility that all hedge fund strategies exhibit idiosyncratic risk in a high volatility regime and find that the joint probability jumps from approximately 0% to almost 100% only during the Long-Term Capital Management (LTCM) crisis. Out-of-sample forecasting tests confirm the economic importance of accounting for the presence of market volatility regimes in determining hedge funds risk exposure.

- by Monica Billio
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- Econometrics, Statistics, Risk Management, Hedge Funds

We investigate why spreads on corporate bonds are so much larger than expected losses from default. Systematic factors make very little contribution to spreads, even if higher moments or downside effects are taken into account. Instead we find that sizes of spreads are strongly related to idiosyncratic-risk factors: not only to idiosyncratic equity volatility, but even more to idiosyncratic bond

- by Gordon Gemmill
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- Applied Mathematics, Value at Risk, Credit Spread, Liquidity

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in , including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work.

- by Damiano Brigo
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- Computational Finance, Papers, Counterparty Risk, Default Risk

In this paper we analyze the slope of the term structure of credit spreads. We investigate the explanatory role of interest rate, market and idiosyncratic equity variables, that recent empirical literature has highlighted as important determinants of credit spread levels. This study extends the analysis further and assesses their impact on credit slopes. We find that these factors impact credit spreads at short and long maturities in a significantly different way. A closer inspection of the credit spread slope also reveals that it is a useful indicator of the direction of changes in future short-term credit spreads. This evidence has important implications for the trading and risk management of portfolios of bonds with different maturities. J a n -0 0 J u l -0 0 J a n -0 1 J u l -0 1 basis points CS Level CS Slope CS Curvature . Time series of level, slope, and curvature of the credit spread term structure for A-rated financial bonds (basis points).

- by Lara Cathcart
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- Risk Management, Financial, Credit Spread, Interest Rate

The emergence of CDS indices and corresponding credit risk transfer markets with high liquidity and narrow bid-ask spreads has created standard benchmarks for market credit risk and correlation against which portfolio credit risk models can be calibrated. Integrated risk management for correlation dependent credit derivatives, such as single-tranches of synthetic CDOs, requires an approach that adequately reflects the joint default behavior in the underlying credit portfolios. Another important feature for such applications is a flexible model architecture that incorporates the dynamic evolution of underlying credit spreads. In this paper, we present a model that can be calibrated to quotes of CDS index-tranches in a statistically sound way and simultaneously has a dynamic architecture to provide for the joint evolution of distance-to-default measures. This is accomplished by replacing the normal distribution by smoothly truncated α-stable (STS) distributions in the Black/Cox version of the Merton approach for portfolio credit risk. This is possible due to the favorable features of this distribution family, namely, consistent application in the Black/Scholes no-arbitrage framework and the preservation of linear correlation concepts. The calibration to spreads of CDS index tranches is accomplished by a genetic algorithm. Our distribution assumption reflects the observed leptokurtic and asymmetric properties of empirical asset returns since the STS distribution family is basically constructed from α-stable distributions. These exhibit desirable statistical properties such as domains of attraction and the application of the generalized central limit theorem. Moreover, STS distributions fulfill technical restrictions like finite (exponential) moments of arbitrary order. In comparison to the performance of the basic normal distribution model which lacks tail dependence effects, our empirical analysis suggests that our extension with a heavy-tailed and highly peaked distribution provides a better fit to tranche quotes for the iTraxx IG index. Since the underlying implicit modeling of the dynamic evolution of credit spreads leads to such results, this suggests that the proposed model is appropriate to price and hedge complex transactions that are based on correlation dependence. A further application might be integrated risk management activities in debt portfolios where concentration risk is dissolved by means of portfolio credit risk transfer instruments such as synthetic CDOs.

- by Jochen Papenbrock
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- Risk Management, Applied Economics, Genetic Algorithm, Credit Risk

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence, hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits finite dimensional Markovian structures. The model also accommodates a correlation structure between the stochastic volatility, default-free interest rates and credit spreads. Defaultfree and defaultable bonds are explicitly priced and an approach for pricing credit default swaps and swaptions is presented where the credit swap rates can be approximated by defaultable bond prices with varying maturities. A sensitivity analysis capturing the impact of the model parameters including correlations and stochastic volatility, on the credit swap rate and the value of the credit swaption is also presented.

- by Samuel Maina
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- Sensitivity Analysis, Mathematical Sciences, Stochastic Volatility, Credit Spread

This paper studies in some examples the role of information in a default-risk framework.

- by Monique Jeanblanc
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- Mathematical Sciences, Credit Risk, Incomplete Information, Credit Spread
- by Kay Giesecke
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- Financial Economics, Great Depression, Developing Country, Credit Risk

We study the effect of financial crises on hedge fund risk. Using a regime-switching beta model, we separate systematic and idiosyncratic components of hedge fund exposure. The systematic exposure to various risk factors is conditional on market volatility conditions. We find that in the high-volatility regime (when the market is rolling-down and is likely to be in a crisis state) most strategies are negatively and significantly exposed to the Large-Small and Credit Spread risk factors. This suggests that liquidity risk and credit risk are potentially common factors for different hedge fund strategies in the down-state of the market, when volatility is high and returns are very low. We further explore the possibility that all hedge fund strategies exhibit a high volatility regime of the idiosyncratic risk, which could be attributed to contagion among hedge fund strategies. In our sample this event happened only during the Long-Term Capital Management (LTCM) crisis of 1998. Other crises including the recent subprime mortgage crisis affected hedge funds only through systematic risk factors, and did not cause contagion among hedge funds.

- by Monica Billio
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- Risk Management, Hedge Funds, Financial Crisis, Credit Risk

- by Amit Alok
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- Credit Spreads, Credit Risk, Credit Spread, Probability of Default

We reject the hypothesis that investment and commercial banks have identical loanpricing policies. We find that compared to commercial banks, investment banks lend to less profitable, more leveraged firms, price riskier classes of term loans more generously, and offer relatively longer-term credits, usually with term, not commitment contracts. Investment banks typically establish higher credit spreads, although the premium declines when a commercial bank joins as syndicate co-arranger. Investment banks also price riskier classes of term loans more generously to borrowers than do commercial banks. Commercial-bank funding advantages do not appear to be a source of the pricing differences.

- by Ha-chin Yi and +1
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- Financial management, Investment Banking, Profitability, Credit Spread

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. We identify global and regional fluctuations in international private debt flows to emerging and developing countries using data on cross border loans and international bond issuance over 1993-2009. We estimate the effects of individual borrower characteristics as well as macroeconomic conditions on the cost of foreign borrowing and test whether these effects differ across phases of the lending cycle. We find that public and financial institutions benefit from lower spreads compared to private and nonfinancial firms and that lenders may differentiate the risk associated with the borrower's industrial sector between good and bad times. The loan (bond) rating has an equally robust spread reduction effect across credit cycle phases. The results also suggest that international reserve holdings and investment ratios have a significant effect on reducing credit spreads for loans, while higher reserve holdings and longer maturities matter more for bond spreads.

- by Johanna Francis
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- Business, Economics, Applied Economics, Emerging Market

In this paper we develop structural first passage models (AT1P and SBTV) with time-varying volatility and characterized by high tractability, moving from the original work of Tarenghi (2004, 2005) [19] and . The models can be calibrated exactly to credit spreads using efficient closed-form formulas for default probabilities. Default events are caused by the value of the firm assets hitting a safety threshold, which depends on the financial situation of the company and on market conditions. In AT1P this default barrier is deterministic. Instead SBTV assumes two possible scenarios for the initial level of the default barrier, for taking into account uncertainty on balance sheet information. While in and [15] the models are analyzed across Parmalat's history, here we apply the models to exact calibration of Lehman Credit Default Swap (CDS) data during the months preceding default, as the crisis unfolds. The results we obtain with AT1P and SBTV have reasonable economic interpretation, and are particularly realistic when SBTV is considered. The pricing of counterparty risk in an Equity Return Swap is a convenient application we consider, also to illustrate the interaction of our credit models with equity models in hybrid products context.

- by Damiano Brigo
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- Monte Carlo Simulation, Risk Management, Counterparty Risk, Calibration

Credit default swap (CDS) spreads display pronounced regime specific behaviour. A Markov switching model of the determinants of changes in the iTraxx Europe indices demonstrates that they are extremely sensitive to stock volatility during periods of CDS market turbulence. But in ordinary market circumstances CDS spreads are more sensitive to stock returns than they are to stock volatility. Equity hedge ratios are three or four times larger during the turbulent period, which explains why previous research on single-regime models finds stock positions to be ineffective hedges for default swaps. Interest rate movements do not affect the financial sector iTraxx indices and they only have a significant effect on the other indices when the spreads are not excessively volatile. Raising interest rates may decrease the probability of credit spreads entering a volatile period.

- by Carol Alexander
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- Applied Mathematics, CDS, Credit Spread, Hedging
- by Ramaprasad Bhar
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- Kalman Filter, State Space, Default Risk, Credit Spread

SummaryThe recent Great Recession has been particularly remarkable not only for its unprecedented severity, but also for the exceptional degree of global interdependence in financial and real variables. A much‐discussed channel of propagation hinges on the international exposure of the balance sheet of highly leveraged players to ‘toxic’ US assets. Yet, existing evidence on the role of exposure is mixed at best. This paper argues that under financial integration, the fact that leveraged investors face the same returns across internationally traded assets, would tend to equalize their borrowing cost across countries. Model simulations show that an unexpected increase in credit spreads in one country generates a similar increase in credit spreads in other financially integrated countries bringing about a global contraction, quite independently of the exposure to foreign assets in the balance sheet of leveraged investors. Our analysis thus suggests some caution in assessing the risks of ‘contagion’ on the exclusive basis of quantitative measures of integration based on cross‐border balance sheet exposure.— Luca Dedola and Giovanni Lombardo

- by Giovanni Lombardo
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- Economics, Economic policy, Credit Spread, Financial Integration

We explore whether governments may have faced scenarios of self-fulfilling prophecy and multiple equilibria during Europe’s sovereign debt crisis. To this end, we estimate the effect of interest rates and other macroeconomic variables on sovereign debt ratings, and of ratings on interest rates. We detect a nonlinear effect of ratings on interest rates which is strong enough to permit multiple equilibria. The good equilibrium is stable, ratings are excellent and interest rates are low. A second unstable equilibrium marks a threshold beyond which the country slides towards an insolvency trap. Coefficient estimates suggest that countries should stay well within the A segment of the rating scale in order to remain safe from being driven towards default.

- by Manfred Gärtner
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- Sovereign Debt, Crisis, Credit Spreads, Credit Spread

Three of the authors previously developed a model to predict the duration of Chapter 11 bankruptcy and the payoff to shareholders . This work augments that study using a much larger sample to reestimate the model and assess its stability. It also provides an opportunity for out-of-sample testing of predictive accuracy. The resulting models are based on Cox's proportional hazards model and the current article points to the need to test two important assumptions underlying the model. First, that the hazards are proportional and, second, that censoring is independent of the event studied. Using the extended data set, all the previously significant accounting variables drop out of the model and only two covariates of the original model remain significant. These are the market wide credit spread and the market capitalization of the firm, both measured immediately prior to the firm's entry to Chapter 11. Receiver operating characteristic curves are then used to assess the predictive accuracy of the original and extended models. The results show that Lachenbruch tests can provide a misleading indication of predictive ability out of sample. Using the Lachenbruch method of in-sample testing, both models show predictive power, but in a true out-of-sample test they fail dismally. The lessons of this work are relevant to better predicting the gains and losses likely to accrue to shareholders of companies in Chapter 11 bankruptcy and in similar administrative arrangements in other jurisdictions.

- by Graham Partington
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- Survival Analysis, Abacus, Event Study, Credit Spread

We examine the link between volume and liquidity in money markets where there are close substitutes. We fi nd that the size of the market, as a proxy for trading volume, affects yield spreads over T-bill rates. We examine the bankers acceptances market, when market size declined by half over the decade of the 1990s. Controlling for interest-rate levels, day-of-the-week, calendar, term structure, credit spread, time-series, and cross-equation effects, we fi nd that the substitution effect does not eliminate the impact of market-size changes on rates, but it does preserve the hierarchy of rates across instruments.

- by Drew Winters
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- Time Series, Financial management, Credit Spread, Financial Market

This paper investigates whether information asymmetry aects,corporate bond credit spreads. To gauge the extent of information asymmetry, we use decomposed equity in- stitutional ownership based on the past investment and trading styles (Bushee(1998, 2001)). First, we detect that dierent institutional groups are associated with firms with varying degrees of information asymmetry. Moreover, we find that decomposed IOs contribute to

- by Gaiyan Zhang
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- Time Series, Credit Spread, Cross Section, Yield Spread
- by Kay Giesecke
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- Applied Mathematics, Copulas, Case Study, Incomplete Information

This analysis tests the price discovery relationship between sovereign CDS premia and bond yield spreads on the same reference entity. The theoretical no-arbitrage relationship between the two credit spreads is confronted with daily data from six Euro-area countries over the period 2004-2011. As a first step, the supposed non stationarity of the two series is verified. Then, we examine whether the non-stationary CDS and bond spreads series are bound by a cointegration relationship. Overall the cointegration analysis confirms that the two prices should be equal to each other in equilibrium, as theory predicts. Nonetheless the theoretical value [1, -1] for the cointegrating vector is rejected, meaning that in the short run the cash and synthetic market's valuation of credit risk differ to various degrees. The VECM analysis suggests that the CDS market moves ahead of the bond market in terms of price discovery. These findings are further supported by the Granger Causality Test: for most sovereigns in the sample, past values of CDS spreads help to forecast bond yield spreads. Short-run deviations from the equilibrium persist longer than it would take for participants in one market to observe the price in the other. That is consistent with the hypothesis of imperfections in the arbitrage relationship between the two markets.

- by Richard Portes
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- Asset Pricing, International Finance, Price Discovery, Developing Country
- by Per Erik Bjertnaes
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- Economic Theory, Economic policy, Risk Management, Capital Structure

- by sally wang
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- Law, Risk Management, Financial Analysis, Standard Deviation

We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer's assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfect-information case, there exists a default-arrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided.

- by Monique Jeanblanc
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- Marketing, Econometrics, Economic Theory, Credit Risk

We estimate the risk and expected returns of private equity investments based on the market prices of exchange-traded funds of funds that invest in unlisted private equity funds. Our results indicate that the market expects unlisted private equity funds to earn abnormal returns of approximately 1% per year. We also find that the market expects listed private equity funds to

- by Roman Kräussl and +1
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- Private Equity, Developing Country, Credit Spread, GDP Growth

This paper empirically examines the aggregate determinants of the credit spread and the influence of monetary policy shocks on its dynamics in Korea. Using the innovations accounting technique from an estimated vector autoregression (VAR) model, we provide a set of interesting results on the short run and the medium run determinants of the credit spread and its dynamics. The key

- by David Kim
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- Economics, Monetary Policy, Vector Autoregression, Default Risk

We consider counterparty risk for Credit Default Swaps (CDS) in presence of correlation between default of the counterparty and default of the CDS reference credit. Our approach is innovative in that, besides default correlation, which was taken into account in earlier approaches, we also model credit spread volatility. Stochastic intensity models are adopted for the default events, and defaults are connected through a copula function. We find that both default correlation and credit spread volatility have a relevant impact on the positive counterparty-risk credit valuation adjustment to be subtracted from the counterparty-risk free price. We analyze the pattern of such impacts as correlation and volatility change through some fundamental numerical examples, analyzing wrong-way risk in particular. Given the theoretical equivalence of the credit valuation adjustment with a contingent CDS, we are also proposing a methodology for valuation of contingent CDS on CDS.

- by Damiano Brigo
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- Mathematical Sciences, Counterparty Risk, Credit Default Swaps, Credit Spread

We would like to thank Francesco Fede and Raffaele Giura for stimulating discussions; any error remains clearly only ours. This is a preliminary and incomplete version. Comments are welcome.

- by Antonio Castagna
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- Credit Spread, Liquidity

In this article we describe what a credit spread option (CSO) is and show a tree algorithm to price it. The tree algorithm we have opted for is a two factor model composed by a Hull and White (HW) one factor for the interest rate process and a Black-Karazinsky (BK) one factor for the default intensity. As opposed to the tree model of Schonbucher 1999 the intensity process cannot become negative. Having as input the risk free yield curve and market implied default probability curve the model by construction will price correctly the associated defaultable bond. We then use Market data to calibrate the model to price an at the money (ATM) CSO call and then test it to price an out of the money (OTM) Bermudan CSO call on a CDS. Furthermore the discussions in this paper show in practice the difficulties and challenges faced by financial institutions in marking to market those

- by Reinaldo Garcia
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- Mathematical Sciences, Credit Spread, Interest Rate, Factor model

Economic theory tells us that market and credit risks are intrinsically related to each other and not separable. We describe the two main approaches to pricing credit risky instruments: the structural approach and the reduced form... more

- by Stuart Turnbull
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- Applied Mathematics, Economic Theory, Risk Management, Credit Risk

1. Introduction 2. Structural Approach 2.1. Basic Assumptions 2.2. Classic Structural Models 2.3. Stochastic Interest Rates 2.4. Credit Spreads: A Case Study 2.5. Comments on Structural Models 3. Intensity-Based Approach 3.1. Hazard Function 3.2. Hazard Processes 3.3. Martingale Approach 3.4. Further Developments 3.5. Comments on Intensity-Based Models 4. Dependent Defaults and Credit Migrations 4.1. Basket Credit Derivatives 4.2. Conditionally Independent Defaults 4.3. Copula-Based Approaches 4.4. Jarrow and Yu Model 4.5. Extension of the Jarrow and Yu Model 4.6. Dependent Intensities of Credit Migrations 4.7. Dynamics of Dependent Credit Ratings 4.8. Defaultable Term Structure 4.9. Concluding Remarks References

- by Tomasz Bielecki
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- Credit Rating, Credit Risk, Case Study, Credit Spread

The price of defaultable or credit-risky bonds differs from the equivalent maturity price of a riskfree bond for a well identified number of factors: the positive probability of default prior to the bond maturity, the estimated loss given default, that depends on the adopted assumption on the recovery rate for that class, see Duffie and Singleton [Duffie, D., Singleton, K.J., 1999. Modeling term structures of defaultable bonds. Rev. Financ. Stud. 12, 687-720] for several models of recovery rates, the probability that the bond issuer will migrate from the current rating class to a lower class. In this study we apply two well-known modelling approaches, due to Jarrow et al. [Jarrow, R.A., Lando, D., Turnbull, S.M., 1997. A Markov model for the term structure of credit risk spreads. Rev. Financ. Stud. 10, 481-523] and Schö nbucher [Schö nbucher, P.J., 2002. A tree implementation of a credit spread model for credit. J. Comput. Finance 6 (2), 175-196] to price specifically two risk sources affecting the evolution of bond prices over time: the risk to move from a current risk class to a different one over the bond residual life, and the risk associated with comovements of the credit spread curves and the risk-free term structure. The former is referred to as transition risk, the latter as correlation risk. The analysis is conducted extending appropriately to a multinomial setting the classical discrete binomial model of the term structure formulated by Black et al. . A one-factor model of interest rates and its application to treasury bond options. Financ. Analysts J. (January/February), 33-39], applied previously by Abaffy et al. [Abaffy, J., Bertocchi, M., Dupačová, J., Moriggia, V., 2000. On generating scenarios for bond portfolios. Bull. Czech 0378-4266/$ -see front matter Ó Econom. Soc. 11, 3-27, and references ibidem] and many other authors in literature. The generalised model, with transition [by Jarrow et al.] and correlation risk [by Schö nbucher]

- by Giorgio Consigli
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- Applied Mathematics, Computational Finance, Credit Risk, Credit Spread
- by Darrell Duffie
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- Finance, Economics, Sovereign Debt, Perceived Risk

In this paper, we extend the framework of Leland (1994b) who proposed a structural model of roll-over debt structure in a Black-Scholes framework to the case of a double exponential jump diffusion process. We consider a trade-off model with firm's parameters as firm risk, riskfree interest rate, payout rate as well as tax benefit of coupon payments, default costs, violation of the absolute priority rule and tax rebate. We obtain the equity, debt, firm and credit spreads values in closed form formulae. We analyze these values as functions of coupon, leverage and maturity.

- by Monique Jeanblanc
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- Credit Spread, Interest Rate, Structural model
- by Henry Schellhorn
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- Modeling, Management Science, Queueing theory, Risk Management

Credit Rating Agencies (CRAs) report information about the credit risk of fixed income securities. The various ways the information is used by financial, legal and regulatory entities may potentially influence the nature of the information production process. Bond ratings are not only used to assess risk, they are also used for regulatory certification, e.g. to classify securities into investment grade (IG) and high yield (HY, or junk) status. These classifications in turn influence institutional demand and serve as bright-line triggers in corporate credit arrangements and regulatory oversight. Regulations may mandate insurance companies and banks to keep much higher reserve capital for high yield issues than for investment grade corporate bonds. Other institutions like pension funds and mutual funds are often restricted by their charters in the amount of HY debt they can hold. Taken together, more than half of all corporate bonds are held by institutions that are subject to rating-based restrictions on their holdings of risky credit assets (Campbell and Taksler (2003)). Lower demand for high yield bond can significantly increase the cost of borrowing for those issuers and is related to capital structure decisions (see Ellul, Jotikasthira and Lundblad (2009), Kisgen and Strahan (2009), Kisgen (2006, 2009)). The institutional and regulatory importance of credit ratings to issuers and investors has raised questions about whether the current system provides the proper incentives for issuers to fully disclose value-relevant information, and for investors to invest in research about credit risk. Using a sample from 2000-2008, we document that almost all large, liquid US corporate bond issues are rated by both S&P and Moody's. Fitch typically plays the role of a "third opinion" for large bond issues 1. During the time period the most prevalent institutional rule used for classifying rated bonds was that, if an issue has two ratings, only the lower rating could be used to classify the issue (e.g. into investment-grade or non-investment grade). However, for issues with three ratings, the middle rating should be used (see, for example, the NAIC guidelines or the Basel II accord). 2 Therefore, if S&P and Moody's ratings are on opposite sides of the investment grade boundary, the Fitch rating (assuming it is the marginal, third rating) is the 'tie-breaker' and will decide into which class the issue falls. Moreover, this rule directly implies that adding a third rating cannot worsen the regulatory rating classification, but could potentially lead to a higher one. Consistent with this option, we find that in about 25% of Fitch rating additions, the addition leads to a regulatory rating improvement, i.e., the resulting middle rating is higher than the lowest rating before the Fitch rating addition. Ex ante, such an improvement would be particularly important when S&P and Moody's ratings are on opposite sides of the investment grade boundary. Absent the improving third rating, the split between S&P and Moody's would result in a classification of high yield. Thus, the value of the Fitch rating is that

- by William Goetzmann
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- Developing Country, Credit Spreads, Credit Rating, Credit Ratings

In this paper, we propose a new risk model to better address events like the recent credit crisis. First, the possible start of a crisis is modeled by including a low-probability jump process. Second, the risk characteristics of the crisis are captured by allowing for time-varying volatilities and correlations. Time variation in correlations is due to the changing importance of two sources: monetary shocks leading to a positive stock-bond correlation, and risk aversion (or "flight to safety") shocks leading to a negative stock-bond correlation. The model stays within the essentially affine class, thereby allowing for closed-form solutions for arbitrage-free nominal and real bond prices of all maturities. Moreover, equity options and swaption prices are included in the estimation procedure to enhance the proper modeling of the volatility on the equity and interest rate markets. The model captures a large part of the time variation in financial risks for pension funds due to both changing volatilities and correlations.

- by Rob van Den Goorbergh and +1
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- Stock Market, Risk Aversion, Credit Spread, Interest Rate

This paper extends the Fama and French (FF) three factor model in studying timevarying risk premiums of Sector Select Exchange Traded Funds (ETFs) under a Markov regime-switching framework. First, we augment the original FF model to include three additional macro factors-market volatility, yield spread, and credit spread. Then, we extend this augmented FF model to a model with a Markov regime switching mechanism for bull, bear, and transition market regimes. We find all market regimes are persistent with the bull market regime being the most persistent and the bear market regime being the least persistent. Both the risk premiums of the Sector Select ETFs and their sensitivities to the risk factors are highly regime dependent. The regime-switching model has a superior performance in capturing the risk sensitivities of the Sector Select ETFs that would otherwise be missed by both the FF and the augmented FF models. JEL Codes: G12, G13, G17, C13

- by Kuan Xu
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- Markov Processes, Risk Management, Control system, Managerial Finance