Credit derivatives with multiple debt issues

We evaluate the most actively traded types of credit derivatives within a unified pricing framework that allows for multiple debt issues. Since firms default on all of their obligations, total debt is instrumental in the likelihood of default and therefore in credit derivatives valuation. We use a single factor interest rate model where the exponential default frontier is based on total debt and is made coherent with observed bond prices. Analytical formulae are derived for credit default swaps, total return swaps (both fixed-for-fixed and fixed-for-floating), and credit risk options (CROs). Price behaviors and hedging properties of all these credit derivatives are investigated. Simulations document that credit derivatives prices may be significantly affected by terms of debt other than those of the reference obligation. The analysis of CROs indicates their superior ability to fine-tune the hedging of magnitude and arrival risks of default.     

How well do classical credit risk pricing models fit swap transaction data?

Currency and interest rate swaps are subject to a complex, two-sided default risk. Several theoretical papers have recently addressed the problem of pricing this swap credit risk. We implement a recent credit risk pricing model in an attempt to evaluate one of the main lines of research in theoretical credit risk analysis. We compare the model's analytical results to actual transaction data thanks to a unique academic database on swap transaction data.     

Exploring the components of credit risk in credit default swaps

In this paper, we test the influence of various fundamental variables on the pricing of credit default swaps. The theoretical determinants that are important for pricing credit default swaps include the risk-free rate, industry sector, credit rating, and liquidity factors. We suggest a linear regression model containing these different variables, especially focusing on liquidity factors. Unlike bond spreads which have been shown to be inversely related to liquidity (i.e., the greater the liquidity, the lower the spread), there is no a priori reason that the credit default swap spread should exhibit the same relationship. This is due to the economic characteristics of a credit default swap compared to a bond. Our empirical result shows that all the fundamental variables investigated have a significant effect on the credit default swap spread. Moreover, our findings suggest that credit default swaps that trade with greater liquidity have a wider credit default swap spread.     

A mathematical model for multi-name credit based on community flocking

We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking system. Based on the flocking model, we compute credit curves for individual names and default time distributions. We also apply the proposed model to the pricing of credit derivatives such as credit default swaps and collateralized debt obligations.     

Currency total return swaps: valuation and risk factor analysis

Abstract

Currency total return swaps (CTRS) are hybrid derivative instruments that allow us to simultaneously hedge against credit and currency risks. We develop a structural credit risk model to evaluate CTRS premia. An empirical test on a sample of 23,005 price observations from 59 underlying issuers yields an average percentage error of around 10%. This indicates that, beyond interest rate risk, firm-specific factors are major drivers of the variations in the valuation of these instruments. Regression analysis of residuals shows that exchange rate determinants account for up to 40% of model pricing errors, indicating that a currency risk premium affects the CTRS price significantly but only marginally, which confirms the prevalence of credit risk in the pricing of CTRS.     

Pricing Derivatives on Financial Securities Subject to Credit Risk

This article provides a new methodology for pricing and hedging derivative securities involving credit risk. Two types of credit risks are considered. The first is where the asset underlying the derivative security may default. The second is where the writer of the derivative security may default. We apply the foreign currency analogy of Jarrow and Turnbull (1991) to decompose the dollar payoff from a risky security into a certain payoff and a “spot exchange rate.” Arbitrage-free valuation techniques are then employed. This methodology can be applied to corporate debt and over the counter derivatives, such as swaps and caps.     

American step-up and step-down default swaps under Lévy models

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Lévy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Lévy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.     

Risk management of deposit insurance corporations with risk-based premiums and credit default swaps

In this paper, we propose a risk-based model for deposit insurance premiums and provide the closed-form formula for premiums, including early closure, capital forbearance, interest rate risk, and moral hazard. Our numerical analysis confirms the proposed pricing formula and the relative impact of the provisions for deposit insurance premiums. We illustrate how to use credit default swaps (CDSs) to manage the bank’s asset risk corresponding to the deposit insurance model. A failed bank, Washington Mutual, is used to demonstrate how to calibrate the model’s parameters and calculate fair premiums that are consistent with market risks on the basis of our proposed model and credit derivatives. Finally, a numerical experiment is designed to determine the optimal hedge ratio, which can minimise the variance of cash-flow of the deposit insurance corporations.     

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.     

The term structure of interbank risk

We infer a term structure of interbank risk from spreads between rates on interest rate swaps indexed to the London Interbank Offered Rate (LIBOR) and overnight indexed swaps. We develop a tractable model of interbank risk to decompose the term structure into default and non-default (liquidity) components. From August 2007 to January 2011, the fraction of total interbank risk due to default risk, on average, increases with maturity. At short maturities, the non-default component is important in the first half of the sample period and is correlated with measures of funding and market liquidity. The model also provides a framework for pricing, hedging, and risk management of interest rate swaps in the presence of significant basis risk.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

Interest Rate Swaps and Corporate Financing Choices

This paper describes the firm's decision to borrow short-term versus long-term and shows how the introduction of interest rate swaps affects this choice. The model shows that in the absence of a swap market, interest rate uncertainty can lead firms to substitute long-term for short-term financing. However, when swaps exist, there is a tendency for firms that expect their credit quality to improve to borrow short-term and use swaps to hedge interest rate risk. The model suggests that, while the demand for fixed for floating swaps is enhanced, the demand for floating for fixed swaps is reduced by the presence of asymmetric information.     

Credit variance risk premiums

This paper studies variance risk premiums in the credit market using a novel data set of swaptions quotes on the CDX North America Investment Grade and High-Yield indices. The returns of credit variance swaps are negative and economically large, irrespective of the credit rating class. They are robust to transaction costs and cannot be explained by established risk factors and structural model variables. We also dissect the overall variance risk premium into receiver and payer variance risk premiums. We show that credit variance risk premiums are mainly driven by the payer corridor, which is associated with worsening macroeconomic conditions.     

Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk

In this research, we investigate the impact of stochastic volatility and interest rates on counterparty credit risk (CCR) for FX derivatives. To achieve this we analyse two real-life cases in which the market conditions are different, namely during the 2008 credit crisis where risks are high and a period after the crisis in 2014, where volatility levels are low. The Heston model is extended by adding two Hull–White components which are calibrated to fit the EURUSD volatility surfaces. We then present future exposure profiles and credit value adjustments (CVAs) for plain vanilla cross-currency swaps (CCYS), barrier and American options and compare the different results when Heston-Hull–White-Hull–White or Black–Scholes dynamics are assumed. It is observed that the stochastic volatility has a significant impact on all the derivatives. For CCYS, some of the impact can be reduced by allowing for time-dependent variance. We further confirmed that Barrier options exposure and CVA is highly sensitive to volatility dynamics and that American options’ risk dynamics are significantly affected by the uncertainty in the interest rates.     

Rapid and accurate development of prices and Greeks for nth to default credit swaps in the Li model

New techniques are introduced for pricing nth to default credit swaps in the Li model. We demonstrate the use of importance sampling to greatly increase the rate of convergence of Monte Carlo simulations for pricing. This technique is combined with the likelihood ratio and pathwise methods for computing the sensitivities of these products to changes in the hazard rates of the underlying obligors. In particular the extension of the pathwise method has wider significance in that it is shown that the method can be used even when the pay-off is discontinuous.     

The determinants of CDS spreads: evidence from the model space

We apply Bayesian model averaging and a frequentistic model space analysis to assess the pricing determinants of credit default swaps (CDSs). Our study focuses on the complete model space of plausible models and thus supports ultimate robustness. Using a large dataset of CDS contracts we find that CDS price dynamics can be mainly explained by factors describing firms’ sensitivity to extreme market movements. More precisely, our results suggest that dynamic copula based measures of tail dependence incorporate most essential pricing information, making other potential determinants such as Merton-type factors or linear variables measuring the systematic market evolution negligible.     

Financial statement comparability and credit risk

Prior research shows that firms’ financial statement comparability improves the accuracy of market participants’ valuation judgments and thus may reduce firms’ costs of capital. Distinct from prior research focusing on the equity market, we develop measures of comparability relevant to debt market participants based on the within-industry variability of Moody’s adjustments to reported accounting numbers for the purposes of credit rating. We examine two sets of adjustments: (1) to the interest coverage ratio and (2) to non-recurring income items. We validate these comparability measures by providing evidence that greater comparability is associated with lower frequency and magnitude of split ratings by credit rating agencies. We predict and find that greater comparability is associated with (1) lower estimated bid-ask spreads for traded bonds, (2) lower credit spreads for both bonds and five-year credit default swaps, and (3) a steeper one- to five-year credit default swap term structure. Our results are consistent with financial statement comparability reducing debt market participants’ uncertainty about and pricing of firms’ credit risk.     

Pricing Derivatives using the Asymptotic Expansion Approach: Credit Migration Models with Stochastic Credit Spreads

The purpose of this paper is to evaluate the asymptotic approximation formulas for the price of contingent claims with credit risk, such as credit default swaps and options on defaultable bonds, in a Markovian credit migration model. Often the generator matrix of a credit migration process is assumed to be deterministic; however, a stochastically varying generator matrix is used in this paper. To apply such a model to the valuation of options on defaultable bonds, the small disturbance asymptotic expansion approach of Kunitomo and Takahashi is used in this study.     

Counterparty Risk and the Pricing of Defaultable Securities

Motivated by recent financial crises in East Asia and the United States where the downfall of a small number of firms had an economy-wide impact, this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty. In this model, firms have correlated defaults due not only to an exposure to common risk factors, but also to firm-specific risks that are termed "counterparty risks." Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps.     

Cross country linkages and transmission of sovereign risk: Evidence from China’s credit default swaps

China’s climb to a trading powerhouse has changed its position in the world and therefore its relationships with other economies. As a result, its sovereign credit risk, which we measure by the pricing of its credit default swaps (CDS), now has the potential to greatly impact other sovereign CDS spreads. Employing a dynamic approach, we find that changes in China’s sovereign risk has strong contagion effects on its goods and service providers, while China is vulnerable to contagion effects from its major importers, suggesting sovereign risk spills over to other regions via the global supply chain. China’s success hurts some of the weaker countries in Europe by competing for their customers, while China faces strong competition itself from its export-focused neighbors. FDI and portfolio investment also affect the CDS relationships between China and other economies.