Credit Derivatives in an Affine Framework

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. Vienna Institute of Finance is funded by WWTF (Vienna Science and Technology Fund).     

Default Clustering Risks in Commercial Mortgage-Backed Securities

This paper proposes an intensity-based pricing model with default dependence structure for CMBS bonds. Three features are incorporated into the proposed model. First, default is a Poisson jump process defined by a function of mortgage rating information. Second, property risks are modeled using a high dimensional Brownian motion process that captures both systematic risk and idiosyncratic risk in property value. Third, default dependence structure is built into the extended model. Based on a set of input parameters, we simulate various pricing effects on a hypothetical CMBS using the proposed model structure. The results of the base-line intensity model show that yield spreads on CMBS bonds increase in the recovery rate, but decreases in the hazard rate. Security structured with smaller subordination tranche exposes CMBS bonds to higher default risks. The model predicts that default clustering increases required yield spreads of CMBS bonds. At a 70% recovery rate and a 3% default hazard rate, yield spreads of Junior bonds are expected to increase by 169 basis points when counterparty risks increase by 50%. The results highlight the importance of clustering risks associated with counterparty default when valuing CMBS bonds.     

Pricing counterparty default risks: Applications to FRNs and vulnerable options

This paper provides simple closed-form pricing models for floating-rate notes and vulnerable options under the counterparty risk framework of [Jarrow, R., Yu, F., 2001. Counterparty risk and the pricing of default risk. Journal of Finance 56, 1765-1799]. After deriving closed-form pricing models for them, this paper illustrates the impact of the default intensity of counterparty on the prices of floating-rate notes and vulnerable options. Numerical examples show that the default risk of counterparty is an important factor of the value of floating-rate notes and vulnerable options.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

Counterparty risk and funding: immersion and beyond

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.     

A framework to measure integrated risk

A framework underlying various models that measure the credit risk of a portfolio is extended in this paper to allow the integration of credit risk with a range of market risks using Monte Carlo simulation. A structural model is proposed that allows interest rates to be stochastic and provides closed-form expressions for the market value of a firm's equity and its probability of default. This model is embedded within the integrated framework and the general approach illustrated by measuring the risk of a foreign exchange forward when there is a significant probability of default by the counterparty. For this example moving from a market risk calculation to an integrated risk calculation reduces the expected future value of the instrument by an amount that could not be calculated using the common pre-settlement exposure technique for estimating the credit risk of a derivative.     

巨灾风险证券化中的操作风险及其控制途径

巨灾风险证券化是把巨灾保险风险转化为衍生证券,销售给金融市场上的投资者,以此实现巨灾保险风险向资本市场的分散转移。但受信息不对称、触发机制等因素影响,巨灾风险证券化这种复杂的技术手段也会引起一些操作风险,如道德风险、基差风险、信用风险等。通过完善信息披露机制、合理选择触发方式、强化巨灾证券的交易保证金要求、加强监管等措施,可以有效地降低巨灾风险证券化过程中的各种风险,促进其平稳健康发展。     

Neglected Risk in Financial Innovation: Evidence from Structured Product Counterparty Exposure

We investigate the compensation of counterparty exposure in the prices of structured products. Our analysis reveals that product issuers did not compensate retail investors for counterparty exposure before the Lehman default. Post-Lehman, retail prices have no longer neglected this risk. We also measure retail investor attention towards issuer credit risk. For a given level of issuer credit risk, counterparty exposure is compensated more when attention is higher. Furthermore, issuers tend to construct products with larger counterparty exposure. Overall, our results shed light on the conditions under which financial engineering generates neglected risk.     

Bilateral credit valuation adjustment for large credit derivatives portfolios

We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity framework, allowing default correlation through a common jump process. The key insight behind our approach is an explicit characterization of the portfolio exposure as the weak limit of measure-valued processes associated with survival indicators of portfolio names. We validate our theoretical predictions by means of a numerical analysis, showing that counterparty adjustments are highly sensitive to portfolio credit risk volatility as well as to the intensity of the common jump process.     

Does the Riskiness of R&D Outweigh Its Benefits? The Perspective of US Private Lenders

We investigate the relationship between R&D investments and loan spread. Prior research documents that R&D is associated with greater future benefits and risks, suggesting that the valuation of R&D depends on a tradeoff between the two. Some research finds that bondholders consider that the benefits of R&D outweigh its risks: R&D is negatively associated with bond yields. This is surprising given that debt holders are more concerned about downside risk due to asymmetric payoffs. Using data on private debt from the US, we find an overall positive association between loan spread and R&D intensity, suggesting that the riskiness of R&D appears to outweigh its benefits for private lenders. Furthermore, an asymmetric payoff structure implies that the risks of R&D for lenders increase with default risk. Consistent with this argument, we find a positive association between R&D and loan spread for firms that are smaller, with high default‐risk ratings, unrated (no public debt), or in industries with weaker legal protection. Unrated firms are in the most R&D‐intensive group and make up nearly 60% of the firms with private debt. Consequently, studies that exclude unrated firms are likely to present an incomplete picture of the perspective of debt holders on R&D.     

Credit risk modeling strategies: the road to serfdom?

This paper aims at presenting some practical issues in modeling default risk of a single commercial credit counterparty from the perspective of a large retail bank. We define default risk as the probability that a counterparty’s intrinsic credit quality deteriorates within a given time horizon such that contractual agreements cannot be honored. This work gives an insight into using scoring/rating models in a credit environment of a large European bank. Contrary to many banks, we did not define the segments in a first step with a view to developing the rating tools in a second step. Our approach has, to some extent, followed a different path. Iteratively, we both defined the borders for a particular segment and selected an appropriate rating tool. More particularly, customer segmentation has been carried out on the basis of various rating tools’ goodness-of-fit criteria. The topics cover customer segmentation using goodness-of-fit measures, data measurement levels and optimization algorithms, rating tool calibration to the central default tendency and communication to the end user. Copyright © 1999 John Wiley & Sons, Ltd.     

Earnouts: The real value of disagreement in mergers and acquisitions

Earnout agreements link part of the payment for an acquired company to its future performance. Despite their option-like features, they cannot be valued using vanilla option-pricing methods. Two peculiar sources of risk affect these contracts: Bidder default before the earnout expiration (default risk) and potential litigation associated with earnouts (litigation risk). We developed an option-pricing model that encompasses these sources of risk, showing that counterparty and litigation risk can have a remarkable impact on earnout values. Our model's relevance is further enhanced by recent accounting standards that require contingent payments to be valued at fair value.     

The Default Risk of Swaps

We characterize the exchange of financial claims from risky swaps. These transfers are among three groups: shareholders, debtholders, and the swap counterparty. From this analysis we derive equilibrium swap rates and relate them to debt market spreads. We then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders. In a simplified case, we obtain closed-form solutions for the value of the default risk in the swap. For interest-rate swaps, we obtain numerical solutions for the equilibrium swap rate, including default risk. We compare these with equilibrium debt market default risk spreads.     

Credit Contagion from Counterparty Risk

Standard credit risk models cannot explain the observed clustering of default, sometimes described as "credit contagion." This paper provides the first empirical analysis of credit contagion via direct counterparty effects. We find that bankruptcy announcements cause negative abnormal equity returns and increases in CDS spreads for creditors. In addition, creditors with large exposures are more likely to suffer from financial distress later. This suggests that counterparty risk is a potential additional channel of credit contagion. Indeed, the fear of counterparty defaults among financial institutions explains the sudden worsening of the credit crisis after the Lehman bankruptcy in September 2008.     

The use of credit default swaps by bond mutual funds: Liquidity provision and counterparty risk

Corporate bond mutual funds increased their selling of credit protection in the credit default swaps (CDS) market during the 2007–2008 financial crisis. This trading activity was primarily in multi-name CDS, greater among larger and established funds, and directed toward counterparty dealers in financial distress. Funds that sold credit protection during the crisis experienced greater credit market risk and superior post-crisis performance, consistent with higher expected returns from liquidity provision. Funds using Lehman Brothers as a counterparty experienced abnormal outflows and returns of –2% immediately following Lehman's bankruptcy, suggesting that funds’ opportunistic trading in CDS exposed investors to counterparty risk.     

Risk assessment based on the analysis of the impact of contagion flow

This paper presents a new framework to model and calibrate the process of firm value evolution when an unanticipated exogenous event impacting one firm can contagiously affect other firms. The nature of propagation of such contagion is determined by the underlying connections between firms, which can adversely affect the tail risks of firm value, hence the securities issued by the firm. This paper combines the insights gained from the existing firm-value models and historical events into a structural model for flow of contagion among firms using a network-based approach. Rather than using stylized networks, we develop a data-driven approach for network construction where we define and calibrate several contagion variables to model the spread of contagion. This framework is applied for assessing firm-level risk under downside risk measures. Using actual data, our model illustrates how connections between firms can lead to heavy-tailed default distributions and default clustering observed in practice.     

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

自由现金流量创造力与违约风险——来自A股公司的经验证据

本文基于我国A股上市公司数据,研究了企业自由现金流量创造力与违约风险之间的关系。研究发现:(1)企业自由现金流量创造力越强,其违约风险越低。经过一系列稳健性检验后,该结论依旧成立。(2)自由现金流量创造力越强的企业往往有更低的债务规模、更高的资产收益率和更低的股票波动,因而其违约风险更低。(3)自由现金流量创造力与违约风险的负相关关系,主要存在于货币政策紧缩时期以及外部信息环境较差的企业。本文发现意味着,监管部门和投资者应重视上市公司自由现金流量创造力不足所带来的潜在债务违约风险,通过不断提高公司自由现金流量创造力,助力我国宏观经济与微观企业高质量发展。     

Effect of rollover risk on default risk: Evidence from bank financing

We study the effect of rollover risk on the risk of default using a comprehensive database of U.S. industrial firms during 1986–2013. Dependence on bank financing is the key driver of the impact of rollover risk on default risk. Default risk and rollover risk present a significant positive relation in firms dependent on bank financing. In contrast, rollover risk is uncorrelated with default probability in the case of firms that do not rely on bank financing. Our measure of rollover risk is the amount of long-term debt maturing in one year, weighted by total assets. In the case of a firm that depends on bank financing, an increase of one standard deviation in this measure leads to a significant increase of 3.2% in its default probability within one year. Other drivers affecting the interaction between rollover risk and default risk are whether a firm suffers from declining profitability and has poor credit. Additionally, rollover risk's impact on default probability is stronger during periods when credit market conditions are tighter.