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.     

Valuation of default-sensitive claims under imperfect information

We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [2001]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.      

The Default Premium and Corporate Bond Experience

The development of organized markets for speculative-grade corporate debt has provided financial researchers with an opportunity to examine the pricing of default risk. By incorporating previous work on the default experience of low-rated corporate debt, this paper presents an introduction to risk-neutral models of risky-bond pricing and uses these to examine the relationship between the default premium embodied in bond yields and actual default rates. The contribution of macroeconomic information to the default premium is also examined. The author finds that holders of low-grade bonds have, on average, been compensated for losses due to default.     

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.      

Asymmetric Correlation and Volatility Dynamics among Stock, Bond, and Securitized Real Estate Markets

We apply a multivariate asymmetric generalized dynamic conditional correlation GARCH model to daily index returns of S&P500, US corporate bonds, and their real estate counterparts (REITs and CMBS) from 1999 to 2008. We document, for the first time, evidence for asymmetric volatilities and correlations in CMBS and REITs. Due to their high levels of leverage, REIT returns exhibit stronger asymmetric volatilities. Also, both REIT and stock returns show strong evidence of asymmetries in their conditional correlation, suggesting reduced hedging potential of REITs against the stock market downturn during the sample period. There is also evidence that corporate bonds and CMBS may provide diversification benefits for stocks and REITs. Furthermore, we demonstrate that default spread and stock market volatility play a significant role in driving dynamics of these conditional correlations and that there is a significant structural break in the correlations caused by the recent financial crisis.     

The composition of CMBS risk

This paper identifies the put-option, liquidity availability proportion, and shadow liquidity risk premia embedded within commercial mortgage backed securities (CMBS) using reduced form and structural generalization models. These risk values are then interpreted as trading signals which are tested with automated trading strategies that buy undervalued and sell overvalued CMBS from November 2007 through June 2015. All three signals generate substantial positive trading profits in testing for the reduced form model but not for the structural generalization. The risk signals constructed independently of market pricing provide more profitable automated trading insights than those constructed from interactions between modeled risk measures and market spreads. In my tests of the information content of the risk signals with respect to future macroeconomic indicators, I find statistically significant evidence in keeping with recent studies. While I cannot reject CMBS efficiency, this paper’s disclosure of new risk measures, the profitability of automated strategies based on those risk measures, and the statistical significance of their forward guidance capabilities, together contributes to our understanding of CMBS risk and the credit spread puzzle debate.     

Pricing credit card loans with default risks: a discrete-time approach

The main purpose of this paper is to modify the Jarrow and van Deventer model by using Das and Sundaram (Manag Sci 46:46–62, 2000) model to extend the Heath–Jarrow–Morton (J Finan Quant Anal 25:419–440, 1990) term-structure model to facilitate the consideration of default risks for pricing credit card loans. Furthermore, we derive closed-form solutions within a continuous-time framework. In addition, we also provide a numerical method for the evaluation of credit card loans within a discrete-time framework. Using the market segmentation argument to describe the characteristics of the credit card industry, our simulation results show that the shapes of the forward rate and forward spread (default risk premium) term structures play extremely important roles in determining the value of credit card loans.     

Asymmetric information,adverse selection,and the pricing of CMBS

We demonstrate that asymmetric information between sellers (loan originators) and purchasers (investors and securities issuers) of commercial mortgages gives rise to a standard lemons problem, whereby portfolio lenders use private information to liquidate lower quality loans in commercial mortgage-backed securities (CMBS) markets. Conduit lenders, who originate loans for direct sale into securitization markets, mitigate problems of asymmetric information and adverse selection in loan sales. Our theory provides an explanation for the pricing puzzle observed in CMBS markets, whereby conduit CMBS loans are priced higher than portfolio loans, despite widespread belief that conduit loans are originated at lower quality. Consistent with theoretical predictions of a lemons discount, our empirical analysis of 141 CMBS deals and 16,760 CMBS loans shows that, after controlling for observable determinants of loan pricing, conduit loans enjoyed a 34 basis points pricing advantage over portfolio loans in the CMBS market.     

Value Creation through Securitization: Evidence from the CMBS Market

Despite recent volatility and constraints in secondary market funding, analysts have ascribed substantial value creation to the securitization of commercial mortgages. Such value creation likely emanates from liquidity enhancements, regulatory arbitrage, price discrimination and risk diversification by pooling and tranching, gains from specialization in origination, servicing, and holding of mortgages, and the like. Indeed, such value creation would be consistent with past accelerated growth in the mortgage- and asset-based securities markets and the sizable profits earned by secondary market intermediaries. In this paper, we estimate the pricing effects of commercial mortgage securitization. We do so by applying loan level data from 1992–2003 to compare the pricing of conduit and portfolio loans held in CMBS structures. In contrast to portfolio loans, which are held for investment by originating institutions, conduit loans are originated for the sole purpose of sale and securitization in the secondary market. If securitization creates value, it should be evidenced in the relative pricing of conduit loans sold into CMBS pools and in a lower cost of capital to loan originators. We estimate a reduced-form model, in which the interest rate spread between commercial mortgages and comparable-maturity treasury securities varies with loan characteristics, capital market conditions, and conduit loan status. Estimation results indicate that securitization of conduit loans leads to an 11 basis points reduction in commercial mortgage interest rates. We assess robustness of results via hazard model tests for omitted variables and originator-specific effects. We further estimate a simultaneous equations model that accounts for the potential endogeneity of mortgage loan terms to the mortgage-treasury rate spread. Results of that analysis suggest a larger 20 basis points reduction in loan pricing among conduit loans sold into CMBS structures.     

CMBS Subordination,Ratings Inflation,and Regulatory‐Capital Arbitrage

Using detailed origination and performance data on a comprehensive sample of commercial mortgage‐backed security (CMBS) deals, along with their underlying loans and a set of similarly rated residential mortgage‐backed securities (RMBS), we apply reduced‐form and structural modeling strategies to test for regulatory‐capital arbitrage and ratings inflation in the CMBS market. We find that the spread between CMBS and corporate‐bond yields fell significantly for ratings AA and AAA after a loosening of capital requirements for highly rated CMBS in 2002, whereas no comparable drop occurred for lower rated bonds (which experienced no similar regulatory change). We also find that CMBS rated below AA upgraded to AA or AAA significantly faster than comparable RMBS (for which there was no change in risk‐based capital requirements). We use a structural model to investigate these results in more detail and find that little else changed in the CMBS market over this period except for the rating agencies' persistent reductions in subordination levels between 1997 and late 2007. Indeed, had the 2005 vintage CMBS used the subordination levels from 2000, there would have been no losses to the senior bonds in most CMBS structures.     

Estimating Default Probabilities of CMBS Loans with Clustering and Heavy Censoring

This paper provides a comprehensive default estimation of commercial real estate loans with a complete commercial mortgage backed securities (CMBS) loan history database. Standard survival models assume that eventually every observation will experience the event. However, often there is a high proportion of censored observation in the sample. A mixture model is proposed to disentangle the probability of “long-term survivorship” and the timing of default occurrence. Loans within the same geographical area and property type tend to exhibit correlation in default incidence. A multilevel model is proposed to capture this correlation within and between clusters.

Municipal Bond Liquidity and Default Risk

This paper examines the pricing of municipal bonds. I use three distinct, complementary approaches to decompose municipal bond spreads into default and liquidity components, and find that default risk accounts for 74% to 84% of the average spread after adjusting for tax‐exempt status. The first approach estimates the liquidity component using transaction data, the second measures the default component with credit default swap data, and the third is a quasi‐natural experiment that estimates changes in default risk around pre‐refunding events. The price of default risk is high given the rare incidence of municipal default and implies a high risk premium.     

Pricing Bonds and Bond Options with Default Risk

The pricing of bonds and bond options with default risk is analysed in the general equilibrium model of Cox, Ingersoll, and Ross (1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk. The general pricing model for defaultable zero-coupon bond is first derived in a simple discrete-time setting and then in continuous-time. The availability of an integrated model allows for the pricing of default-free options written on defaultable bonds and of vulnerable options written either on default-free bonds or defaultable bonds. A comparison between our results and those given by Jarrow and Turnbull (1995) is also presented.     

极端气候对商业银行风险承担的影响——来自中国地方性商业银行的经验证据

深化对气候相关金融风险的认识,对于促进绿色低碳发展,防范系统性金融风险具有重要意义。本文以2004—2018年期间281家中国地方性商业银行为样本,实证检验了极端气候对银行风险承担的影响及其机制。研究发现,极端强降水气候显著提升了银行风险承担,极端高温和极端低温气候对银行风险承担不存在明显影响。极端强降水主要通过给银行信贷主体带来经济损失,影响违约概率和银行信贷资产质量,进而影响银行风险承担水平;提高灾前的保险保障水平、强化碳减排机制以及确保银行资本的充足性均有利于弱化极端气候对银行风险承担的影响;相较于以地级和省会城市工商业和居民为主要服务对象的地方性商业银行,极端强降水对以“三农”为主要服务对象的县域地方性商业银行风险承担的影响更大。因此,提升商业银行应对极端气候风险意识,提高气候灾害保险保障水平,强化碳减排机制和银行资本充足管理,均有利于降低极端气候对银行风险的影响。     

Uncertain inflation,exchange rates,and bond yields

The yields on international bonds are affected by exchange rate risk and country risk, in addition to factors such as default and duration that are relevant in the pricing of domestic bonds. This paper constructs a theory of bond yields in a single period framework, with the risk of nominal bonds being endogenous to the model. The behaviour of the monetary authority is modelled explicitly and is shown to be a crucial determinant of the risk of nominal bonds. A distinction is made between the risk of default in the usual sense, and the risk of being paid in currency which is worth less in real terms, with the type of risk that is relevant in a particular case depending on the monetary policy followed. The implications of results for exchange rate risk are also explored in a world where Purchasing Power Parity holds.     

Distressed debt prices and recovery rate estimation

This paper has two purposes. First, it uses distressed debt prices to estimate recovery rates at default. In this regard, estimates are obtained for three recovery rate models: recovery of face value, recovery of Treasury, and recovery of market value. We show that identifying the “economic” default date, as distinct from the recorded default date, is crucial to obtaining unbiased estimates. The economic default date is defined to be the first date when the market prices the firm’s debt as if it has defaulted. An implication is that the standard industry practice of using 30-day post default prices to compute recovery rate yields biased estimates. Second, we construct and estimate a distressed debt pricing model. We use this model to implicitly estimate the parameters of the embedded recovery rate process and to price distressed debt. Our distressed debt pricing model fits market prices well, with an average pricing error of less than one basis point.      

Estimating Default Probabilities Implicit in Commercial Mortgage Backed Securities (CMBS)

This paper uses a structural credit risk model, providing an analytical formula to estimate default probabilities implicit in commercial mortgage backed security prices. Empirical studies of CMBS default have focused on the probability of default depending on loan characteristics at the origination and market indices. Recent studies show that unobservable current loan-to-value (LTV) ratio is a key state variable driving default. We update this variable using Real Estate Investment Trust (REIT) property-type indices over time. Later, we employ first passage time approach to study CMBS default using implied LTV.

Catastrophe Risk Bonds

Abstract

This article examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore, the pricing of catastrophe risk bonds requires an incomplete markets setting, and this creates special difficulties in the pricing methodology. The authors briefly discuss the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.     

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.     

Measuring large comovements in financial markets

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.