Restructuring risk in credit default swaps: An empirical analysis

This paper estimates the price for restructuring risk in the US corporate bond market during 1999–2005. Comparing quotes from default swap (CDS) contracts with a restructuring event and without, we find that the average premium for restructuring risk represents 6%–8% of the swap rate without restructuring. We show that the restructuring premium depends on firm-specific balance-sheet and macroeconomic variables. And, when default swap rates without a restructuring event increase, the increase in restructuring premia is higher for low-credit-quality firms than for high-credit-quality firms. We propose a reduced-form arbitrage-free model for pricing default swaps that explicitly incorporates the distinction between restructuring and default events. A case study illustrating the model’s implementation is provided.     

An uncooperative order model for items with trade credit,inventory-dependent demand and limited displayed-shelf space

This paper considers a two-echelon supply chain where a supplier sells a single product through a retailer, who faces an inventory-dependent demand. The supplier hopes to incentive the retailer to order more items by offering trade credit. The retailer places the ordered items on the display shelf (DS) with limited space and stocks the remaining items (if any) that exceed the shelf capacity in his/her backroom/warehouse (BW). From the supplier’s perspective, we focus mainly on under which conditions the supplier should offer trade credit and how he/she should design such trade credit policy and corresponding ordering policy to obtain much more benefits. From the retailer’s perspective, we discuss whether the retailer needs BW and exactly how many items need to be stocked in BW when the supplier offers trade credit. We formulate a “supplier-Stackelberg” game model, from which we obtain the conditions under which the presented simple trade credit policy not only increases the overall chain profit but also each member’s profit. We also show that the trade credit policy is always more beneficial to the retailer than to the supplier if it is offered.     

General dynamic term structures under default risk

We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this requires the introduction of an additional term in the forward rate approach by Heath et al. (1992). This term is driven by a random measure encoding information about those times where default can happen with positive probability. In this framework, we derive necessary and sufficient conditions for a reference probability measure to be a local martingale measure for the large financial market of credit risky bonds, also considering general recovery schemes.     

Default barrier intensity model for credit risk evaluation

We establish the Default Barrier Intensity (DBI) model, based on the conditional survival probability (also called hazard function barrier), which allows the pricing of credit derivatives with stochastic parameters. Moreover, the DBI is an analytic model which combines the structural and the reduced form approaches. It deals with the impact of the default barrier intensity on the processes around the firm. Using this model we prove the Doob–Meyer decomposition of the default process associated with the random barrier. In this framework, we present the default barrier process as the sum of its compensator (which is a predictable process) and a martingale related to the smallest filtration making the random barrier a stopping time. Furthermore, the DBI as well as the Shifted Square Root Diffusion (SSRD) Alfonsi’s model emphasizes on the dependence between the stochastic default intensity and the interest rate. This model can be useful since it can be easily generalized to all the credit derivatives products such as Collateralized Debt Obligations (CDO) and Credit Default Swaps (CDS).     

An inventory system with two suppliers and default risk

This paper considers the problem of joint replenishment and pricing for a single product with two suppliers and supply disruption. Our objective is to maximize the total profit by choosing an appropriate replenishment and pricing policy. We not only obtain that the form of the optimal policy has a (s,S,p,σ,Σ)-type, but also analyze how supply disruption affects the profit function and the optimal policy.     

The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management

Min et al. [1] (J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285.) develop an inventory model for deteriorating items under stock-dependent demand and two-level trade credit. They provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximize the retailer’s average profit per unit time. Basically, their paper is correct and interesting. Recently, several researchers have been showing a huge interest in developing simple and easy to implement solution procedures in management science. Therefore this paper indicates that Min et al.’s solution procedure can be further improved and simplified. So, the main purpose of this paper is to present simple and easy to understand solution procedures to locate the optimal solutions of an inventory model that considers deteriorating items under stock-dependent demand and two-level trade credit.     

The inventory models under conditional trade credit in a supply chain system

In several recent investigations dealing with the economic order quantity with permissible delay in payments, the following assumptions are made:     

A review of trade credit literature: Opportunities for research in operations

Trade credit arises when a buyer delays payment for purchased goods or services. Its nature has predominantly been an area of inquiry for researchers from the disciplines of finance, marketing, and economics but it has received relatively little attention in other domains. In our article, we provide an integrative review of the existing literature and discuss conflicting study outcomes. We organize the relevant literature into seven areas of inquiry and analyze four in detail: trade credit motives, order quantity decisions, credit term decisions, and settlement period decisions. Additionally, we derive a detailed agenda for future research in these areas.     

Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing

In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of S periods, and the retailer in turn provides a trade credit of R periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, and (c) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights.     

Comparison results for exchangeable credit risk portfolios

This paper is dedicated to risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding mixture distributions. Thus we can proceed to some comparisons between stop-loss premiums, CDO tranche premiums and convex risk measures on aggregate losses. This methodology provides a unified analysis of dependence for a number of CDO pricing models based on factor copulas, multivariate Poisson and structural approaches.     

Effects of risk aversion and decision preference on equilibriums in supply chain finance incorporating bank credit with credit guarantee

We constructed a Stackelberg game in a supply chain finance (SCF) system including a manufacturer, a capital‐constrained retailer, and a bank that provides loans on the basis of the manufacturer's credit guarantee. To emphasize the financial service providers' risks, we assumed that both the bank and the manufacturer are risk‐averse and formulated trade‐off objective functions for both of them as the convex combination of the expected profit and conditional value‐at‐risk. To explore the effects of the risk preferences and decision preferences on SCF equilibriums, we mathematically analyzed the optimal order quantities, wholesale prices, and interest rates under different risk preference scenarios and performed numerical analyses to quantify the effects. We found that incorporating bank credit with a credit guarantee can effectively balance the retailer's financing risk between the bank and the manufacturer through interest rate charging and wholesale pricing. Moreover, SCF equilibriums with risk aversion are highly affected by the degree of both the lender's and guarantor's risk tolerance in regard to the borrower's default probability and will be more conservative than those in the risk‐neutral cases that only maximize expected profit.     

Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity

Recently, Min et al. [18] established an inventory model for deteriorating items under stock-dependent demand and two-level trade credit and obtained the optimal replenishment policy. Their analysis imposed a terminal condition of zero ending-inventory. However, with a stock-dependent demand, it may be desirable to order large quantities, resulting in stock remaining at the end of the cycle, due to the potential profits resulting from the increased demand. As a result, to make the theory more applicable in practice, we extend their model to allow for: (1) an ending-inventory to be nonzero, (2) a maximum inventory ceiling to reflect the facts that too much stock leaves a negative impression on the buyer and the amount of shelf/display space is limited.     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.     

A multicriteria approach for rating the credit risk of financial institutions

Within the new bank regulatory context, the assessment of the credit risk of financial institutions is an important issue for supervising authorities and investors. This study explores the possibility of a developing risk assessment model for financial institutions using a multicriteria classification method. The analysis is based on publicly available financial data for UK firms. The results indicate that the proposed multicriteria methodology provides promising results compared to well known statistical methods.     

Model combination for credit risk assessment: A stacked generalization approach

The development of credit risk assessment models is often considered within a classification context. Recent studies on the development of classification models have shown that a combination of methods often provides improved classification results compared to a single-method approach. Within this context, this study explores the combination of different classification methods in developing efficient models for credit risk assessment. A variety of methods are considered in the combination, including machine learning approaches and statistical techniques. The results illustrate that combined models can outperform individual models for credit risk analysis. The analysis also covers important issues such as the impact of using different parameters for the combined models, the effect of attribute selection, as well as the effects of combining strong or weak models.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust non-zero-sum investment and reinsurance game with default risk

This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, who are concerned about the potential model ambiguity and aim to seek the robust optimal reinsurance and investment strategies. The ambiguity-averse insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks; and can invest in a financial market consisting of one risk-free asset, one risky asset and one defaultable corporate bond. The objective of each insurer is to maximize the expected exponential utility of his terminal surplus relative to that of his competitor under the worst-case scenario of the alternative measures. Applying the techniques of stochastic dynamic programming, we derive the robust Nash equilibrium reinsurance and investment policies explicitly and present the corresponding verification theorem. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium reinsurance and investment strategies and draw some economic interpretations from these results.     

Optimization of nearest neighbor classifiers via metaheuristic algorithms for credit risk assessment

The classification problem consists of using some known objects, usually described by a large vector of features, to induce a model that classifies others into known classes. The present paper deals with the optimization of Nearest Neighbor Classifiers via Metaheuristic Algorithms. The Metaheuristic Algorithms used include tabu search, genetic algorithms and ant colony optimization. The performance of the proposed algorithms is tested using data from 1411 firms derived from the loan portfolio of a leading Greek Commercial Bank in order to classify the firms in different groups representing different levels of credit risk. Also, a comparison of the algorithm with other methods such as UTADIS, SVM, CART, and other classification methods is performed using these data.     

The inventory model for trade credit in economic ordering policies of deteriorating items in a supply chain system

In 1994, professors Jaggi and Aggarwal presented the economic ordering policies of deteriorating items in the presence of trade credit using a discounted cash-flows (DCF) approach. This paper discusses the same problem as that of Jaggi and Aggarwal and indicates that some approximations to the optimal cycle times proposed by Jaggi and Aggarwal are inappropriate sometimes. A theorem is derived out to find the optimal cycle time. With that theorem, a simple algorithm is developed to locate the optimal cycle time.     

鲁棒信用风险优化的线性锥优化模型

考虑了具有强健性的信用风险优化问题. 根据最差条件在值风险度量信用风险的方法,建立了信用风险优化问题的模型. 由于信用风险的损失分布存在不确定性,考虑了两类不确定性区间,即箱子型区间和椭球型区间. 把具有强健性的信用风险优化问题分别转化成线性规划问题和二阶锥规划问题. 最后,通过一个信用风险问题的例子来说明此模型的有效性.