Pricing inflation-indexed derivatives

In this article, we start by briefly reviewing the approach proposed by Jarrow and Yildirim for modelling inflation and nominal rates in a consistent way. Their methodology is applied to the pricing of general inflation-indexed swaps and options. We then introduce two different market model approaches to price inflation swaps, caps and floors. Analytical formulae are explicitly derived. Finally, an example of calibration to swap market data is considered.     

Pricing the risks of default

This paper decomposes default risk into timing and recovery risks. The two default components are explicitly priced as if they were traded in the futures market. We develop estimation strategies evaluating recovery risks and then construct implicit prices of contingent securities reflecting purely the timing risk. The models are estimated on monthly data for rates on certificates of deposit offered by institutions in the Savings and Loan Industry, during the 1987–1991 period. Empirical results support market expectations of lower likelihoods of default after 1989.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

Pricing of swaps with default risk

In this paper, I study the valuation of interest rate and currency swaps with default risk under the contingent claim analysis framework. I demonstrate that the traditional approach of pricing swap contracts as exchanges of loans underestimates the value of such contracts to the counterparty with higher credit rating and exaggerates the credit spread required to guard against default risk. Numerical simulations show that the swap rate is not sensitive to counterparty credit rating: for a ten year interest rate swap, a one hundred basis point increase in counterparty bond yield spread results in only about one basis point increase in the swap rate. (JEL G10, G12, G13)This paper is based on Chapter 2 of my Ph.D. dissertation at Yale University. I would like to thank my dissertation committee, Kenneth French, Roger Ibbotson, and Jonathan Ingersoll, Jr. (chairman), for helpful advice and guidance. I would also like to thank Keny Back, Richard Lindsey, N. R. Prabhala, Ming Huang, Marti Subrahmanyam, three anonymous referees and especially Bob Jarrow, the editor, for helpful comments and suggestions. Any errors that remain are solely mine. This paper won the 1996 Trefftzs Award for best student paper from the Western Finance Association.     

Covered interest parity with default risk

In this paper we derive a simple model of covered interest parity (CIP) with the assumption that interbank money market rates are risky. The model assumes that the default risk of uncollateralised loans can be hedged perfectly by credit default swap contracts. We show that the no-arbitrage condition is satisfied by a band. The location of this no-arbitrage band depends on the relative riskiness of the two counterparties in the CIP trade. We present evidence on the performance of the model for developed currency pairs in 2008–2011. We find that FX swap spreads (CIP deviations calculated from interbank interest rates of two countries) either fluctuated within the no-arbitrage bands or were close to the edges of the no-arbitrage bands.     

Modeling default risk with support vector machines

Predicting default risk is important for firms and banks to operate successfully. There are many reasons to use nonlinear techniques for predicting bankruptcy from financial ratios. Here we propose the so-called Support Vector Machine (SVM) to predict the default risk of German firms. Our analysis is based on the Creditreform database. In all tests performed in this paper the nonlinear model classified by SVM exceeds the benchmark logit model, based on the same predictors, in terms of the performance metric, AR. The empirical evidence is in favor of the SVM for classification, especially in the linear non-separable case. The sensitivity investigation and a corresponding visualization tool reveal that the classifying ability of SVM appears to be superior over a wide range of SVM parameters. In terms of the empirical results obtained by SVM, the eight most important predictors related to bankruptcy for these German firms belong to the ratios of activity, profitability, liquidity, leverage and the percentage of incremental inventories. Some of the financial ratios selected by the SVM model are new because they have a strong nonlinear dependence on the default risk but a weak linear dependence that therefore cannot be captured by the usual linear models such as the DA and logit models.     

Enterprise risk management in financial groups: analysis of risk concentration and default risk

In financial groups, enterprise risk management is becoming increasingly important in controlling and managing the different independent legal entities in the group. The aim of this paper is to assess and relate risk concentration and joint default probabilities of the group’s legal entities in order to achieve a more comprehensive picture of a financial group’s risk situation. We further examine the impact of the type of dependence structure on results by comparing linear and nonlinear dependencies using different copula concepts under certain distributional assumptions. Our results show that even if financial groups with different dependence structures do have the same risk concentration factor, joint default probabilities of different sets of subsidiaries can vary tremendously.

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.     

National politics and bank default risk in the eurozone

We study the impact of national politics on default risk of eurozone banks as measured by the stock market-based Distance to Default. We find that national electoral cycles, the power of the government as well as the government’s party ideological alignment significantly affect the stability of banks in the eurozone member countries. Moreover, we show that the impact of national politics on bank default risk is more pronounced for large as well as weakly capitalized banks.     

Counterparty credit risk and the credit default swap market

Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced. We examine this issue using an extensive proprietary data set of contemporaneous CDS transaction prices and quotes by 14 different CDS dealers selling credit protection on the same underlying firm. This unique cross-sectional data set allows us to identify directly how dealers' credit risk affects the prices of these controversial credit derivatives. We find that counterparty credit risk is priced in the CDS market. The magnitude of the effect, however, is vanishingly small and is consistent with a market structure in which participants require collateralization of swap liabilities by counterparties.     

Unobserved systematic risk factor and default prediction

We conduct a thorough analysis on the role played by the unobserved systematic risk factor in default prediction. We find that this latent factor outweighs the observed systematic risk factors and can substantially improve the in-sample predictive accuracy at the firm, rating group, and aggregate levels. Thus it might be helpful to include the unobserved systematic risk factor when simulating portfolio credit losses. However, we also find that this factor only marginally improves out-of-sample model performance. Therefore, although the models we investigated all show reasonably good ability to rank order firms by default risk, accurate prediction of default rate remains challenging even when the unobserved systematic risk factor is considered.     

Laying off credit risk: Loan sales versus credit default swaps

How do markets for debt cash flow rights, with and without accompanying control rights, affect the efficiency of lending? A bank makes a loan, learns if it needs monitoring, and then decides whether to lay off credit risk. The bank can transfer credit risk by either selling the loan or buying a credit default swap (CDS). With a CDS, the originating bank retains the loan's control rights; with loan sales, control rights pass to the loan buyer. Credit risk transfer leads to excessive monitoring of riskier credits and insufficient monitoring of safer credits. Increases in banks' cost of equity capital exacerbate these effects. For riskier credits, loan sales typically dominate CDS but not for safer credits. Once repeated lending and consequent reputation concerns are modeled, although CDSs remain dominated by loan sales for riskier credits, for safer credits they can dominate loan sales, supporting better monitoring (albeit to a limited extent) while allowing efficient risk sharing. Restrictions on the bank's ability to sell the loan expand the range in which CDSs are used and monitoring is too low.     

Credit default swap prices as risk indicators of listed German banks

This paper explores empirically the usefulness of credit default swap (CDS) prices as market indicators. The sample of reference entities consists of large, internationally active German banks and the observation period covers 3 years. By analysing the explanatory power of three risk sources: idiosyncratic credit risk, systematic credit risk and liquidity risk, we gain important insights into modeling the dynamics of CDS spreads. The impact of systematic risk, for example, has three components; one is related to the overall state of the economy, another related to the risk of the internationally active banking sector, and the third is an unobservable systematic factor. Default probabilities, inferred from a tractable reduced form model for CDS spreads, are compared with expected default frequencies from the Moody’s KMV model. The results lend empirical support to the hypothesis that structural models can be less informative than reduced-form models of CDS spreads in the case of banks with major investment banking activities as the leverage loses explanatory power. Although the CDS market appears to have matured over the observation period, during certain periods premiums for liquidity risk can increase substantially thus limiting the value of CDS spreads as market indicators. We conclude that equity prices and CDS premia should be considered together to fully exploit the information content of both market indicators and to mitigate their respective drawbacks.

Valuation of reverse mortgages under (limited) default risk

In this paper, we develop a consistent valuation framework for reverse mortgages based on reduced-form intensity models as used in credit risk modelling. Within our modelling framework, we explicitly calculate the probability that the total loan amount exceeds the house value at termination of the contract and derive the maximum payment(s) which can be made to the homeowner under certain constraints. We apply our results to data from the German market and discuss implications for the design of reverse mortgages from a lender's perspective.     

Effects of market default risk on index option risk-neutral moments

We investigate the relative importance of market default risk in explaining the time variation of the S&P 500 Index option-implied risk-neutral moments. The results demonstrate that market default risk is positively (negatively) related to the index risk-neutral volatility and skewness (kurtosis). These relations are robust in the presence of other factors relevant to the dynamics and microstructure nature of the spot and option markets. Overall, this study sheds light on a set of economic determinants which help to understand the daily evolution of the S&P 500 Index option-implied risk-neutral distributions. Our findings offer explanations of why theoretical predictions of option pricing models are not consistent with what is observed in practice and provide support that market default risk is important to asset pricing.     

上市公司违约风险、盈余质量与银行信用借款——基于沪深A股市场的经验研究

本文从静态和动态两个层面研究了会计信息的银行债务契约有用性。实证研究发现,上市公司基于会计信息的违约风险越大,银行信用借款比例越低;盈余质量越差则会显著降低违约风险与信用借款之间的关系;而在区分了长短期信用借款后,上述关系仅存在于短期信用借款之中。进一步研究发现,银企关系的好坏会显著影响长期信用借款的比例。这表明会计信息能降低银行债务契约决策中的信息不对称,但其有用性却受到盈余质量和债务期限的影响。     

Interacting default intensity with a hidden Markov process

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method can be applied to a wide range of problems. Based on this model, we derive the joint distribution of multiple default times without imposing stringent assumptions on the form of default intensities. Closed-form formulas for the distribution of default times are obtained which are then applied to solve a number of practical problems such as hedging and pricing credit derivatives. The method and numerical algorithms presented can be applicable to various forms of default intensities.     

Wimp or tough guy: Sequential default risk and signaling with mortgages

When analyzing what to do with a currently defaulted loan, the lender must consider the impact of his foreclosure versus workout decision on the expected payoff of subsequent loans as well as on the payoff of the current loan. This is because borrowers with future loan payoff dates can observe the lender's actions and update prior information regarding the lender's toughness or wimpiness when dealing with defaulted loans. In this paper we consider the strategic interaction between a lender and multiple borrowers, where borrowers have distinct, sequentially maturing mortgage loans and where the lender has private information regarding the magnitude of his foreclosure costs. We find that a variety of strategic outcomes can occur that explain the co-existence of workout and foreclosure in the mortgage marketplace. In general, the lender's workout/foreclosure response depends on the cost of bluffing (e.g., foreclosing when workout is cheaper) versus the value of reducing expected defaults and workout concession losses on future loans (e.g., imperfect foreclosure cost information leads future borrowers to payoff the mortgage when default would have been optimal under perfect information). Given recently revised expectations regarding the depth of the real estate recession, our results may explain the move by many lenders away from granting workout concessions and toward taking a harder line when dealing with defaulting borrowers.     

An innovative feature selection method for support vector machines and its test on the estimation of the credit risk of default

Support vector machines (SVM) have been extensively used for classification problems in many areas such as gene, text and image recognition. However, SVM have been rarely used to estimate the probability of default (PD) in credit risk. In this paper, we advocate the application of SVM, rather than the popular logistic regression (LR) method, for the estimation of both corporate and retail PD. Our results indicate that most of the time SVM outperforms LR in terms of classification accuracy for the corporate and retail segments. We propose a new wrapper feature selection based on maximizing the distance of the support vectors from the separating hyperplane and apply it to identify the main PD drivers. We used three datasets to test the PD estimation, containing (1) retail obligors from Germany, (2) corporate obligors from Eastern Europe, and (3) corporate obligors from Poland. Total assets, total liabilities, and sales are identified as frequent default drivers for the corporate datasets, whereas current account status and duration of the current account are frequent default drivers for the retail dataset.     

Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model

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 (CDSs), 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.Received: March 2004, Mathematics Subject Classification (2000): 60H10, 60J60, 60J75, 91B70JEL Classification: G13