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India is a major contributor to the global warming of the world, but there persists a prevalent lack of understanding of carbon trading (carbon credit derivative) as a commodity tradable on the stock exchange. The study brings into light the predominant drivers that can lead to the sustainable enhancement of efficacy and efficiency of carbon credit trading in India. The key drivers responsible for the sustainable implementation of the carbon credit derivative trading in India are identified and critically examined. The Analytic Hierarchy Process and Best–Worst Method have been used to rank the factors and sub-factors based on the priority (or weights) provided by the industry experts. The results indicate that the risk factors in the carbon credit derivative market are extremely crucial for enhancing sustainable trading of carbon credit derivatives closely followed by the reward and opportunity factors. The study is the first study which analyses the factors that can lead to the sustainable implementation of carbon credit trading in India. The study also contributes to the organizational strategy that carbon securitization would contribute significantly towards their financial as well as ecological sustainability. [ABSTRACT FROM AUTHOR]

This paper develops a new time-varying mixture copula, in which the dynamic weights of four distinct copulas are determined by a two-stratum process, to investigate the magnitude of tail dependence in four independent quadrants. In the two-stratum process, the weight of each copula is determined firstly by the relative importance of positive and negative dependence structures, and then by its own past values and adjustment processes. The weighting mechanism is time-varying in each stratum. This new specification is applied to analyze the asymmetric tail dependencies between the stock and exchange rate markets. Empirical results show four interesting findings. First, the quasi-maximum likelihood estimation (QMLE) has a better fitting ability than does the inference function for margins. The relative efficiency of the QMLE is irrespective of marginal specifications. Second, the goodness-of-fit tests of the new time-varying mixture copula are crucially affected by the marginal specifications. Third, estimation methods impact mixture weights. Four distinct tail dependencies are observed, revealing the importance of considering all four tails concurrently, and not just parts of the four tails. Fourth, the asymmetric positive and negative dependencies are significant. Each country shows a similar pattern of asymmetric negative dependence, but a different pattern of asymmetric positive dependence. These empirical findings provide important portfolio allocation implications. [ABSTRACT FROM AUTHOR]

We discuss dynamic hedging of counterparty risk for a portfolio of credit derivatives by the local risk-minimization approach. We study the problem from the perspective of an investor who, trading with credit default swaps (CDS) referencing the counterparty, wants to protect herself/himself against the loss incurred at the default of the counterparty. We propose a credit risk intensity-based model consisting of interacting default intensities by taking into account direct contagion effects. The portfolio of defaultable claims is of generic type, including CDS portfolios, risky bond portfolios and first-to-default claims with payments allowed to depend on the default state of the reference firms and counterparty. Using the martingale representation of the conditional expectation of the counterparty risk price payment stream under the minimal martingale measure, we recover a closed-form representation for the locally risk minimizing strategy in terms of classical solutions to nonlinear recursive systems of Cauchy problems. We also discuss applications of our framework to the most prominent classes of credit derivatives. [ABSTRACT FROM AUTHOR]

This paper studies the valuation of the American call-option under the Heston model in two regimes, i.e., fast-mean reverting and slow-mean reverting regimes. In the case of the European-style option under the Heston model, a closed-form solution for one-dimensional integration can be derived. However, in the case of the American-style option, it is impossible to obtain a general analytic integral equation for the price. By using singular and regular perturbation techniques introduced by Fouque et al. (Multiscale stochastic volatility for equity, interest-rate and credit derivative, Cambridge University Press, Cambridge, 2011) and the maturity randomization method introduced by Carr (Rev Financ Stud 11:597–626, 1998), we provide an approximate analytic solution of the American call-option and describe a numerical scheme to evaluate the value of this solution. Numerical results show that our method is accurate and efficient compared to the finite-difference method and the Longstaff and Schwartz (Rev Financ Stud 14(1):113–147, 2001) method. [ABSTRACT FROM AUTHOR]

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear–rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method. [ABSTRACT FROM AUTHOR]

Increment variance reduction techniques are add-ons to Monte Carlo (MC) simulations. They make MC simulations converging faster by repeating the number of simulations with an incremental rate derived from mathematical functions. Besides speeding up MC simulations, the major advantage of increment techniques is their ability to handle large numbers of simulations avoiding memory saturation and overflow which occur when a plain MC simulation is involved in the pricing of multi-name credit derivatives. A trend among authors pricing financial securities with MC simulation has been to choose Quasi-Monte Carlo (QMC) methods using deterministic sequences instead of MC methods involving pseudorandom generators such as congruential generator and Mersenne twister. The Increment family models circumvent the constraint of identifying the optimal QMC sequence to price a given security by using a common generator such as Matlab-LCG-Xor RNG and determining the optimal mathematical function of incrementation of MC simulations that will make the pricing of the security adequate. Market participants in need of selecting a reliable numerical method for pricing complex financial securities such as multi-name credit derivatives will find our paper appealing. [ABSTRACT FROM AUTHOR]

This paper deals with a model for pricing Collateralized Loan Obligations, where the underlying credit risk is driven by a marked Hawkes process, involving both clustering effects on defaults and random recovery rates. We provide a sensitivity analysis of the CLO price with respect to the parameters of the Hawkes process using a change of probability and a variational approach. We also provide a simplified version of the model where the intensity of the Hawkes process is taken as the instantaneous default rate. In this setting, we give a moment-based formula for the expected survival probability. [ABSTRACT FROM AUTHOR]

We develop models for portfolio diversification in the sovereign credit default swaps (CDS) markets and show that, despite literature findings that sovereign CDS spreads are affected by global factors, there is sufficient idiosyncratic risk to be diversified. However, we identify regime switching in the times series of CDS spreads and spread returns, and the optimal diversified strategies can be regime dependent. The developed models trade off the CVaR risk measure against expected return, consistently with the statistical properties of spreads. We consider three investment strategies suited for different CDS market participants: for investors with long positions, speculators that hold uncovered long and short positions, and hedgers with covered long and short exposures. We use the models to illustrate that diversification pays in the CDS market. The models are also tested for active portfolio management in Eurozone core and periphery, and Central, Eastern and South-Eastern Europe countries, and the optimized portfolio results outperform the broad S&P/ISDA Eurozone Developed Nation Sovereign CDS index. The paper concludes by identifying open questions in developing integrated enterprise-wide risk management models using CDS. [ABSTRACT FROM AUTHOR]

In this paper, we explore the features of a structural credit risk model wherein the firm value is driven by normal tempered stable (NTS) process belonging to the larger class of Lévy processes. For the purpose of comparability, the calibration to the term structure of a corporate bond credit spread is conducted under both NTS structural model and Merton structural model. We find that NTS structural model provides better fit for all credit ratings than Merton structural model. However, it is noticed that probabilities of default derived from the calibration of the term structure of a bond credit spread might be overestimated since the bond credit spread could contain non-default components such as illiquidity risk or asymmetric tax treatment. Hence, considering CDS spread as a reflection of the pure credit risk for the reference entity, we calibrate it in order to obtain more reasonable probability of default and obtain valid results in calibration of the market CDS spread with NTS structural model. [ABSTRACT FROM AUTHOR]

In Crépey (Math. Finance 25:23-50, 2015), a basic reduced-form counterparty risk modelling approach was introduced under a standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties. This basic setup, with a related continuity assumption on some of the data at the first default time of the two parties, is too restrictive for wrong-way and gap risk applications, such as counterparty risk on credit derivatives. This paper introduces an extension of the basic approach, implements it through marked default times and applies it to counterparty risk on credit derivatives. [ABSTRACT FROM AUTHOR]

Recent empirical evidences indicate that default rates are influenced not only by the observable or latent risk factors, but also depend on the history of past defaults. Motivated by this empirical finding, we consider in this paper a reduced-form, intensity-based credit risk model, which allows for both frailty and default contagion, using a so-called 'self-exciting' intensity, in the sense that the default intensity varies not only with the risk factors, but also depends on the previous default history of all the firms. With 'self-exciting' default intensity, we are able to obtain closed-form expressions for the pricing of credit derivative securities in our model. The estimation of parameters using the EM algorithm is considered as well. [ABSTRACT FROM AUTHOR]

Correlated default factors and systemic risk are clearly priced in credit portfolio securities such as CDOs or index CDSs. In this paper we study an extensive CDX data set for evidence of whether correlated default factors are also present in the underlying CDS market. We develop a cash-flow-based top-down approach for modeling CDSs from which we can derive the following major contributions: (1) Correlated default factors did not matter for CDS prices prior to the financial crisis in 2008. During and after the crisis, however, their importance increased strongly. (2) We observe that correlated default factors primarily impact on the CDS prices of firms with an overall low CDS level. (3) Idiosyncratic risk factors for each single CDS play a major (minor) role when the CDS premia are high (low). [ABSTRACT FROM AUTHOR]

In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit risk model. We then show how to price credit default swaps (CDSs) and introduce credit valuation adjustment (CVA) as an extension of CDSs. In particular, our model can capture right-way-and wrong-way exposure. This means, we capture the dependence structure of the default event and the value of the transaction under consideration. For simple contracts, we provide closed-form solutions. However, due to the fact that we allow for a dependence between the default event and the value of the transaction, closed-form solutions are difficult to obtain in general. Hence we conclude this paper with a reduced form model, which is more tractable. [ABSTRACT FROM AUTHOR]

We consider N Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion L of variables in a given state converge at rate 1/ N as N → ∞. Based on these results, we propose a multi-level simulation algorithm using a family of sequences with increasing length, to obtain estimators for these expected functionals with a mean-square error of ϵ and computational complexity of order ϵ, independent of N. In particular, this optimal complexity order also holds for the infinite-dimensional limit. Numerical examples are presented for tranche spreads of basket credit derivatives. [ABSTRACT FROM AUTHOR]

We examine a specific portfolio credit derivative, an Asset Protection Scheme (APS), and its applicability as a discretionary regulatory tool to reduce asymmetric information and help restore the capital base of troubled banks. The APS can be a fair-valued contract with an appropriate structure of incentives. We apply two alternative multivariate structural default risk models: the classical Gaussian Merton model and a model based on Normal Inverse Gaussian processes. Using a data set on annual farm level data from 1996 to 2009, we use the Danish agricultural sector as a case study and price an APS on an agricultural loan portfolio. We compute the economic capital for this loan portfolio with and without an APS. Moreover, we illustrate how model risk in the form of parameter uncertainty is reduced when an APS is attached to the loan portfolio. [ABSTRACT FROM AUTHOR]

We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-step procedure, much like in a standard static copula setup. In this sense this solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. This model can be used for any dynamic portfolio credit risk issue, such as dynamic hedging of CDOs by CDSs, or CVA computations on credit portfolios. [ABSTRACT FROM AUTHOR]

The global financial crisis has shown that many financial institutions dealing with credit derivatives were exposed to severe unexpected losses. This indicates that systematic influences are decisively underestimated particularly with regard to structured products like securitized tranches of collateralized debt obligations. Our analytical study addresses these systematic effects: We provide a simple model which allows a closed-form comparison of both bonds and tranches with respect to their systematic risk. We demonstrate that the exposure to systematic risk of tranches may be many times higher than the exposure of bonds, even if both products share the same rating grade, e.g., an 'AAA' rating, measured by either default probability or expected loss. Particularly in economic downturns, default rates of tranches may be multiples of those of bonds. Our results help understand high default rates of tranches during the financial crisis and show that classical ratings are insufficient metrics for measuring risks of structured products. [ABSTRACT FROM AUTHOR]

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks' equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial 'asset shortfall' and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets. [ABSTRACT FROM AUTHOR]

This paper examines the contract interpretation strategies adopted by the International Swaps and Derivatives Association (ISDA) for its credit derivatives contracts in the Greek sovereign debt crisis. We argue that the economic function of sovereign credit default swaps (CDS) after Greece is limited and uncertain, partly thanks to ISDA's insistence on textualist interpretation. Contract theory explanations for textualist preferences emphasise either transactional efficiency or relational factors, which do not fit ISDA or the derivatives market. We pose an alternative explanation: the embrace of textualism in this case may be a means for ISDA to reconcile the competing political demands from state regulators and its market constituents. We describe categories of contracts susceptible to such political demands, and consider when and why textualism might be the preferred response. [ABSTRACT FROM PUBLISHER]

We present a new model of the occurence of credit events such as rating changes and defaults for risk analyses of some portfolio credit derivatives. The framework of our model is based on a so-called top-down approach. Specifically, we first consider modeling the point process of each type of credit event in the whole economy using a self-exciting intensity process. Next, we characterize the point processes of credit events in the underlying sub-portfolio using random thinning processes specified by the distribution of credit ratings in the sub-portfolio. One of the main features of our model is that the model can capture credit risk contagion simultaneously among several credit portfolios. We present a credit event simulation algorithm based on our model and illustrate an application of the model to risk analyses of loan portfolios. [ABSTRACT FROM AUTHOR]

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically ∼ 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulas are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup, market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practical application of the model is discussed: we analyse calibration, the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies. The paper closes with a few numerical case studies. [ABSTRACT FROM AUTHOR]

Equity default swaps (EDS) are hybrid credit-equity products that provide a bridge from credit default swaps (CDS) to equity derivatives with barriers. This paper develops an analytical solution to the EDS pricing problem under the jump-to-default extended constant elasticity of variance model (JDCEV) of Carr and Linetsky. Mathematically, we obtain an analytical solution to the first passage time problem for the JDCEV diffusion process with killing. In particular, we obtain analytical results for the present values of the protection payoff at the triggering event, periodic premium payments up to the triggering event, and the interest accrued from the previous periodic premium payment up to the triggering event, and we determine arbitrage-free equity default swap rates and compare them with CDS rates. Generally, the EDS rate is strictly greater than the corresponding CDS rate. However, when the triggering barrier is set to be a low percentage of the initial stock price and the volatility of the underlying firm's stock price is moderate, the EDS and CDS rates are quite close. Given the current movement to list CDS contracts on organized derivatives exchanges to alleviate the problems with the counterparty risk and the opacity of over-the-counter CDS trading, we argue that EDS contracts with low triggering barriers may prove to be an interesting alternative to CDS contracts, offering some advantages due to the unambiguity, and transparency of the triggering event based on the observable stock price. [ABSTRACT FROM AUTHOR]

The evolution of credit derivatives has inspired many researchers to investigate the behaviour of credit spreads. Today the growing consensus is that the equity option market provides sufficient information to estimate latent credit parameters. Hull et al. (J. Credit Risk 1(1):3-28, ) propose a clever approach to estimate credit spreads from the equity option market. In this paper we first perform a time series analysis to test the conjecture of an existing relationship between credit spreads and implied equity volatility and find strong evidence of a positive relationship. We also propose an extension to Hull et al.'s paper that significantly improves credit spread estimation. [ABSTRACT FROM AUTHOR]

We present a methodology for valuing portfolio credit derivatives under a reduced form model for which the default intensity processes of risk assets follow the one-factor Vasicek model. A closed-form solution of joint survival time distribution is obtained. The solution is applied to value credit derivatives of a credit default swap index and collateralized debt obligation. The limitation of methods using the Vasicek model is discussed. We propose that the method is valid and efficient for a portfolio with small-scale correlated risk assets, for which the acceptable size is much greater than for the traditional method. Numerical examples and parameter analysis are also presented. [ABSTRACT FROM AUTHOR]

This paper considers a general reduced-form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of noisy price observations for traded credit products. In this context the pricing of credit derivatives leads to a challenging nonlinear-filtering problem. We provide recursive updating rules for the filter, derive a finite-dimensional filter for the case where X follows a finite-state Markov chain, and propose a novel particle-filtering algorithm. A numerical case study illustrates the properties of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Under Basel II framework, credit risk assessment is of high significance in the light of correlation risk. Correlation risk is often envisioned along with business conditions and financial market’s impact. We employ copula methodology to identify the dependence structures that may exist between market risk fundamentals and credit risk fundamentals. Considering credit derivative spreads as credit risk fundamentals and market data as market risk determinants, we describe and quantify the asymmetric link prevailing between credit risk and market risk. Credit risk is negatively linked with market price risk whereas it becomes positively linked with market volatility risk. Such patterns give rise to interesting asymmetric dependence structures between both risk sources. We are then able to balance reliably market price risk with market volatility feedback, the market trend supporting a common correlation between securities. In the light of the previous trade-off, we propose also a simple credit risk management rule. [ABSTRACT FROM AUTHOR]

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed. [ABSTRACT FROM AUTHOR]

To study the impact of counter-party default risk of forward contracts on a firm's production and hedging decisions, I use a model of a risk-averse competitive firm under price uncertainty. I find that if expected profits from forward contracts are zero, the hedge ratio is not affected by default risk under general preferences and general price distributions. My analysis shows that if the size of a firm's forward position does not affect the counter-party's default probability, default risk is no reason to reduce hedge ratios. However, a firm's optimal output is negatively affected by default risk, and it is generally advisable to hedge default risk with credit derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the use of interacting particle systems in the computation of probabilities of simultaneous defaults in large credit portfolios. The method can be applied to compute small historical as well as risk-neutral probabilities. It only requires that the model be based on a background Markov chain for which a simulation algorithm is available. We use the strategy developed by Del Moral and Garnier in (Ann. Appl. Probab. 15:2496–2534, ) for the estimation of random walk rare events probabilities. For the purpose of illustration, we consider a discrete-time version of a first passage model for default. We use a structural model with stochastic volatility, and we demonstrate the efficiency of our method in situations where importance sampling is not possible or numerically unstable. [ABSTRACT FROM AUTHOR]

Before the credit crisis that started in mid-2007, it was generally believed by top regulators that credit derivatives make banks sounder. In this paper, we investigate the validity of this view. We examine the use of credit derivatives by US bank holding companies with assets in excess of one billion dollars from 1999 to 2005. Using the Federal Reserve Bank of Chicago Bank Holding Company Database, we find that in 2005 the gross notional amount of credit derivatives held by banks exceeds the amount of loans on their books. Only 23 large banks out of 395 use credit derivatives and most of their derivatives positions are held for dealer activities rather than for hedging of loans. The net notional amount of credit derivatives used for hedging of loans in 2005 represents less than 2% of the total notional amount of credit derivatives held by banks and less than 2% of their loans. We conclude that the use of credit derivatives by banks to hedge loans is limited because of adverse selection and moral hazard problems and because of the inability of banks to use hedge accounting when hedging with credit derivatives. Our evidence raises important questions about the extent to which the use of credit derivatives makes banks sounder. [ABSTRACT FROM AUTHOR]

Portfolio credit derivatives are contracts that are tied to an underlying portfolio of defaultable reference assets and have payoffs that depend on the default times of these assets. The hedging of credit derivatives involves the calculation of the sensitivity of the contract value with respect to changes in the credit spreads of the underlying assets, or, more generally, with respect to parameters of the default-time distributions. We derive and analyze Monte Carlo estimators of these sensitivities. The payoff of a credit derivative is often discontinuous in the underlying default times, and this complicates the accurate estimation of sensitivities. Discontinuities introduced by changes in one default time can be smoothed by taking conditional expectations given all other default times. We use this to derive estimators and to give conditions under which they are unbiased. We also give conditions under which an alternative likelihood ratio method estimator is unbiased. We illustrate the application and verification of these conditions and estimators in the particular case of the multifactor Gaussian copula model, but the methods are more generally applicable. [ABSTRACT FROM AUTHOR]

An efficient method for valuing credit derivatives based on three entities is developed in an affine framework. This includes interdependence of market and credit risk, joint credit migration and counterparty default risk of three firms. As an application we provide closed form expressions for the joint distribution of default times, default correlations, and default swap spreads in the presence of counterparty default risk. [ABSTRACT FROM AUTHOR]

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities. [ABSTRACT FROM AUTHOR]

The pricing problems of credit derivatives have received much attention in the last decade. An important unresolved problem, however, is the pricing of credit derivatives under the general environment in which the interest rate process and the hazard rate process are stochastic. This article addresses the pricing problems of credit derivatives by the asymptotic expansion approach. This approach has only recently been introduced to mathematical finance, and it enables us to evaluate credit derivatives under a widely adapted class of models. We also present a numerical study. [ABSTRACT FROM AUTHOR]

We introduce the two-dimensional shifted square-root diffusion (SSRD) model for interest-rate and credit derivatives with (positive) stochastic intensity. The SSRD is the unique explicit diffusion model allowing an automatic and separated calibration of the term structure of interest rates and of credit default swaps (CDS’s), and retaining free dynamics parameters that can be used to calibrate option data. We propose a new positivity preserving implicit Euler scheme for Monte Carlo simulation. We discuss the impact of interest-rate and default-intensity correlation and develop an analytical approximation to price some basic credit derivatives terms involving correlated CIR processes. We hint at a formula for CDS options under CIR + + CDS-calibrated stochastic intensity. [ABSTRACT FROM AUTHOR]

This paper presents a conceptual and general framework for valuation of single-name credit derivatives. The general subfiltration approach of [J-R] to modelling default risk, which includes the Cox-process setting of [L], is integrated with a numeraire invariant approach. Several known results are reformulated and extended in this framework. New concepts and results are presented for change of numeraire in presence of default and valuation of credit swaptions. A new formula on fractional recovery of pre-default value is derived, generalizing that of [D-S]. A Black-Scholes formula for credit default swaptions due to [S] is shown to serve as a least-squares approximation to the general case. [ABSTRACT FROM AUTHOR]

Recently many kinds of credit derivatives are traded in the market. The default probability implied in the market becomes important to price some credit derivatives. Also it is useful for managing the credit risk because it includes the market information. In this paper we show how to calculate the implied default probability in the default swap market or the defaultable bond market. [ABSTRACT FROM AUTHOR]

In the last two decades, the market of credit derivatives has expanded rapidly, and the importance of pricing problems for credit derivatives has been recognized especially in the last decade. Among these securities, the pricing problems of credit derivatives with an early exercise, such as American put options, have not received enough attention. In view of this need, this paper develops a continuous stochastic model of American put options on defaultable bonds. The method of obtaining a solution is based on a new result of the optimal stopping problem for a diffusion process with a jump. Some characterizations of American put options are provided using partial differential equations. [ABSTRACT FROM AUTHOR]

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions. [ABSTRACT FROM AUTHOR]