Estimating rating transition probabilites with missing data

In this article we provide a rigorous treatment of one of the central statistical issues of credit risk management. GivenK-1 rating categories, the rating of a corporate bond over a certain horizon may either stay the same or change to one of the remainingK-2 categories; in addition, it is usually the case that the rating of some bonds is withdrawn during the time interval considered in the analysis. When estimating transition probabilities, we have thus to consider aK-th category, called withdrawal, which contains (partially) missing data. We show how maximum likelihood estimation can be performed in this setup; whereas in discrete time our solution gives rigorous support to a solution often used in applications, in continuous time the maximum likelihood estimator of the transition matrix computed by means of the EM algorithm represents a significant improvement over existing methods.     

Coordinating contracts for a financially constrained supply chain

We consider a financially constrained supply chain in which a supplier (leader) sells products to a retailer (follower) who has no access to bank financing due to her low credit rating. However, the supplier can borrow from a bank and offer trade credit to the retailer to alleviate her financial constraint. Failure to pay off a bank loan or trade credit incurs a variable default cost. We analyze the centralized version of the supply chain to obtain new coordination requirements. We then examine whether revenue-sharing, buyback, and all-unit quantity discount contracts can coordinate our supply chain. We show that the all-unit quantity discount contract fails to coordinate. However, the revenue-sharing and buyback contracts can coordinate the supply chain, but only when the supply chain has a sufficient total working capital. Moreover, they cannot allocate profit flexibly unless the supplier has a large enough working capital. Finally, we design a generalized revenue-sharing contract that coordinates the supply chain with flexible profit allocation, and also show by numerical examples its superiority over the revenue-sharing and buyback contracts.     

The Econometrics of Piecewise-Linear Budget Constraints

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both unobserved heterogeneity of preferences and measurement error. Econometric issues in estimation and testing are discussed, and the results of the studies that have been conducted to date are surveyed.     

Market-Based Credit Ratings

We present a methodology for rating in real-time the creditworthiness of public companies in the U.S. from the prices of traded assets. Our approach uses asset pricing data to impute a term structure of risk neutral survival functions or default probabilities. Firms are then clustered into ratings categories based on their survival functions using a functional clustering algorithm. This allows all public firms whose assets are traded to be directly rated by market participants. For firms whose assets are not traded, we show how they can be indirectly rated by matching them to firms that are traded based on observable characteristics. We also show how the resulting ratings can be used to construct loss distributions for portfolios of bonds. Finally, we compare our ratings to Standard & Poors and find that, over the period 2005 to 2011, our ratings lead theirs for firms that ultimately default.     

Default and Punishment in General Equilibrium1

We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment by thinking of assets as pools. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of adverse selection and signalling phenomena in a perfectly competitive, general equilibrium framework. Perfect competition eliminates the need for lenders to compute how the size of their loan or the price they quote might affect default rates. It also makes for a simple equilibrium refinement, which we propose in order to rule out irrational pessimism about deliveries of untraded assets. We show that refined equilibrium always exists in our model, and that default, in conjunction with refinement, opens the door to a theory of endogenous assets. The market chooses the promises, default penalties, and quantity constraints of actively traded assets.     

Bidding under auctioneer default risk

In a financially turbulent economy, participants of a procurement auction should consider in their bids the event of default of the auctioneer, which may result to substantial damages for the winning bidder. We examine a sealed bid auction, with private cost values and interdependence among the beliefs of the bidders about the auctioneer׳s default risk. The probability of payment of the bid price by the auctioneer is estimated by each bidder. For a first and a second price auction, we derive equilibrium bidding strategies, which address the risk of default and optimally adjust the bid price, introducing a risk premium in the form of an additional mark-up. A numerical illustration of the proposed strategies is provided. The effect of auctioneer׳s risk of default on the procurement project cost is examined. Financial arrangements that may be used to relax or eliminate the effect of the risk of default, such as early payment methods, third party guarantees or insurance programs are discussed and evaluated in comparison with the approach of risk premium on bid price.     

论数字意象“五”文化缺省及其在翻译中的重构

对于一般的西方文化读者来说，数字“五”的文化意象没有任何联想意义，理解时势必造成文化缺省，因而．在翻译过程中数字意泉“五”的重构就成为译者必须慎之又慎的任务。本文探讨了“五”宇所蕴含的传统汉文化，及其译成英文的方法．     

债权人迟延制度若干问题探讨

债权人迟延是由于债权人的原因而使债务不能履行。认识、分析债权人迟延制度应从该制度的构成要件、法律性质及法律效果着手。我国新合同法体系下没有债权人迟延制度的专门规定,但相关内容涉及了债权人迟延的范畴,指出了债权人迟延的部分效果。解决现行合同法暴露出的问题须通过对合同法解释,同时应该考虑对国内外有关学说的采纳以进一步完善立法。     

Fair Valuation of Life Insurance Contracts Under a Two-Sided Jump Diffusion Model

In this article, we study the fair valuation of participating life insurance contract, which is one of the most common life insurance products, under the two-sided jump diffusion model with the consideration of default risk. The participating life insurance contracts considered here can be expressed as portfolios of options as shown by Grosen and Jøgrgensen (1997 Grosen , A. , Jøgrgensen , P. (1997). Valuation of early exercisable interest rate guarantees. J. Risk Ins. 64:481–503.[Crossref], [Web of Science ®] , [Google Scholar]). We can give the Laplace transforms for these options under the two-sided jump diffusion model, and then price these options by inverting Laplace transforms.