Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

零售商回收电子废弃物条件下的定价模型研究

以废旧手机为例,在分散决策和集中决策条件下建立了零售商单独回收的定价模型.然后,分别求得了在分散决策下的Stackelberg均衡解与集中决策时的最优决策,并作了对比分析.结果表明:集中决策下的系统利润优于分散决策下的系统利润.最后,通过数值验证了相关结论.     

Monetary aspects of acquiring technology for price discrimination of a perishable storable product

The remaining shelf-life of perishable storable products can become an additional source of volatility among consumers and a matter for price discrimination. Two models are presented. Both models assume the retailer has the information about consumers’ sensitivity to the remaining shelf-life (eg, their purchasing history). Only the first assumes the retailer has also the technology for price discrimination. An optimal solution for each model is analytically obtained and a numerical example that illustrates the significance is introduced. Numerical illustration indicates that a policy of identical prices for all based on accurate information about consumer sensitivity to remaining shelf-life results in a profit that is just slightly smaller per unit of time compared with the price discrimination policy. Opposing, the numerical illustration also indicates significant difference between the models with respect to their impact on consumers. Following these results, the regulator may consider suggesting the retailer monetary incentives in order to utilize price discrimination.     

Monte Carlo scenario generation for retail loan portfolios

Monte Carlo simulation is a common method for studying the volatility of market traded instruments. It is less employed in retail lending, because of the inherent nonlinearities in consumer behaviour. In this paper, we use the approach of Dual-time Dynamics to separate loan performance dynamics into three components: a maturation function of months-on-books, an exogenous function of calendar date, and a quality function of vintage origination date. The exogenous function captures the impacts from the macroeconomic environment. Therefore, we want to generate scenarios for the possible futures of these environmental impacts. To generate such scenarios, we must go beyond the random walk methods most commonly applied in the analysis of market-traded instruments. Retail portfolios exhibit autocorrelation structure and variance growth with time that requires more complex modelling. This paper is aimed at practical application and describes work using ARMA and ARIMA models for scenario generation, rules for selecting the correct model form given the input data, and validation methods on the scenario generation. We find when the goal is capturing the future volatility via Monte Carlo scenario generation, that model selection does not follow the same rules as for forecasting. Consequently, tests more appropriate to reproducing volatility are proposed, which assure that distributions of scenarios have the proper statistical characteristics. These results are supported by studies of the variance growth properties of macroeconomic variables and theoretical calculations of the variance growth properties of various models. We also provide studies on historical data showing the impact of training length on model accuracy and the existence of differences between macroeconomic epochs.     

European generic scoring models using survival analysis

Credit scoring discriminates between ‘good’ and ‘bad’ credit risks to assist credit-grantors in making lending decisions. Such discrimination may not be a good indicator of profit, while survival analysis allows profit to be modelled. The paper explores the application of parametric accelerated failure time and proportional hazards models and Cox non-parametric model to the data from the retail card (revolving credit) from three European countries. The predictive performance of three national models is tested for different timescales of default and then compared to that of a single generic model for a timescale of 25 months. It is found that survival analysis national and generic models produce predictive quality, which is very close to the current industry standard—logistic regression. Stratification is investigated as a way of extending Cox non-parametric proportional hazards model to tackle heterogeneous segments in the population.     

The economy and loss given default: evidence from two UK retail lending data sets

Loss given default (LGD) models predict losses as a proportion of the outstanding loan, in the event a debtor goes into default. The literature on corporate sector LGD models suggests LGD is correlated to the economy and so changes in the economy could translate into different predictions of losses. In this work, the role of macroeconomic variables in loan-level retail LGD models is examined by testing the inclusion of macroeconomic variables in two different retail LGD models: a two-stage model for a residential mortgage loans data set and an ordinary least squares model for an unsecured personal loans data set. To improve loan-level predictions of LGD, indicators relating to the macroeconomy are considered with mixed results: the selected macroeconomic variable seemed able to improve the predictive performance of mortgage loan LGD estimates, but not for personal loan LGD. For mortgage loan LGD, interest rate was most beneficial but only predicted better during downturn periods, underestimating LGD during non-downturn periods. For personal loan LGD, only net lending growth is statistically significant but including this variable did not bring any improvement to R².     

Validating the Gravity-Based Competitive Location Model Using Inferred Attractiveness

The attractiveness of retail facilities is an essential component of models analyzing competition among retail facilities. In this paper we introduce an innovative method for inferring retail facility attractiveness. Readily available data from secondary sources about customers' buying power and sales volumes obtained by competing retail facilities are used. The gravity-based competitive facility location model is used to predict sales. The attractiveness of the retail facilities are inferred from these data.The procedure is used to confirm the gravity competitive facility location model. Inferred attractiveness results based on empirical data from Orange County, California, were compared with an independent survey with excellent match.     

A critical comparison of the various plausible inter-echelon gaming processes in supply chain models

An increasing number of supply-chain models are related to the following structure: (i) a manufacturer supplies a product to a retailer—who fixes a retail price and then retails the product to the consumers; (ii) the effect of the retail price on sales volume is dictated by a deterministic demand curve known to both parties. Results from these models depend very much on the ‘gaming process’ that is assumed to govern how the manufacturer and the retailer interact with each other. This paper reviews and compares some basic characteristics of seven seemingly plausible gaming processes; including the two most common ones: the manufacturer-Stackelberg and the fixed-markup-retailer processes. Our results show that: (i) each of the seven processes appear to be no less plausible than the other six; (ii) all seven processes possess some implausible characteristics; (iii) the relationships among the processes are confusing and do not appear to be intuitively logical; (iv) the relationships among these processes are further complicated by the way they are affected by the form of the assumed demand curve. Our results show that in supply-chain modelling more attention should be given to: (i) the proper selection of an appropriate gaming process assumption; (ii) how the model's results change under different gaming processes; (iii) the incorporation of information asymmetry that will allow these gaming-process assumptions to become more realistic.     

The value of competitive information in forecasting FMCG retail product sales and the variable selection problem

Sales forecasting at the UPC level is important for retailers to manage inventory. In this paper, we propose more effective methods to forecast retail UPC sales by incorporating competitive information including prices and promotions. The impact of these competitive marketing activities on the sales of the focal product has been extensively documented. However, competitive information has been surprisingly overlooked by previous studies in forecasting UPC sales, probably because of the problem of too many competitive explanatory variables. That is, each FMCG product category typically contains a large number of UPCs and is consequently associated with a large number of competitive explanatory variables. Under such a circumstance, time series models can easily become over-fitted and thus generate poor forecasting results.     

Locating and capacity planning for retailers of a new supply chain to compete on the plane

This paper investigates the network design problem of a two-level supply chain (SC), which is applicable for industries such as automotive, fuel and tyre manufacturing. Models presented in this paper aim at locating retail facilities of an SC and identifying their required capacities in the presence of existing competing retailers of a rival SC. We consider feasible locating space of the retail facilities on the continuous plane with bounded constraints and static competition among the rivals of the markets with deterministic demands. The problem is used for both essential and luxury product cases; hence, we consider elastic and inelastic demands, both. The models discussed in this paper are non-linear and non-convex which are difficult to solve. We use interval branch-and-bound as optimization algorithm for small size single-retailer problems, but for large-scale, multi-retailer problems we need to have more efficient methods. Therefore, we apply a heuristic algorithm (H1), a simulated annealing (SA) algorithm, an interior point (IP) algorithm, a genetic algorithm (GA) and a pattern search algorithm for solving multi-retailer problem with elastic and inelastic demands. Computational results obtained from performing different solution approaches for both elastic and inelastic show that mostly IP, PS, and H1 methods outperform the other approaches. The computational results on a real-life case are also promising. Several extended mathematical models and an example of a typical case with details are presented in the appendices of the paper.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems

Effective models of key operational decisions in multilocation inventory systems are important for a successful retail sector. This paper argues that much of the existing research in this area is not applicable to a highly competitive retail environment, particularly if periodic review replenishment policies are used. The paper develops a model of a periodic review multilocation inventory system that is suitable for this environment and investigates the characteristics of optimal replenishment and transshipment decisions. This motivates the development of three simple heuristic transshipment policies that are practical for systems with many locations. The results of a numerical study involving systems with five locations suggest that the performance of these heuristic policies is often close to optimal and can be considerably better than the performance of commonly used policies.     

Portfolio adjusting optimization with added assets and transaction costs based on credibility measures

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.     

Networth exposure to interest rate risk: An empirical analysis of Indian commercial banks

In the Basel II era, management of interest rate risk in the banking book has become significant. In the first study of its kind, we develop a simulation based driver-driven approach to estimate the impact of interest rate volatility on the networth of Indian banks during the period 2002–2004. We derive the interest rates that drive changes in deposit and prime lending rates (PLR). Then we perform Monte Carlo simulation and multiple regressions, on these driver rates, to obtain simulated shocks to deposit rates and PLR. We use these simulated shocks to get the 99% worst EVE loss for the sample banks. These losses are much larger than what the existing literature suggests. This is because, apart from repricing risk, we are the first to find evidence of significant basis risk. Our results have important policy implications both for banks and regulators.     

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.     

考虑服务和退货的双渠道供应链定价问题研究

在考虑零售服务和消费者退货情况下,运用两阶段优化方法分别探究了集中式和分散式两种双渠道供应链的最优定价策略。研究发现零售服务有助于提高零售商的渠道权力,并始终使制造商获益,但只有当服务水平小于某一临界值时,才使制造商和零售商同时得到帕累托改进。零售价格和直销价格与退货率正相关,而与服务水平的关系受渠道结构的影响。服务水平的提高加剧了供应链的“双重边际化”效应,制造商通过生产与消费者需求相匹配的产品来降低退货风险可以减弱这种效应,从而提高供应链效率。     

Bundling retail products: Models and analysis

We consider the impact of bundling products on retail merchandising. We consider two broad classes of retail products: basic and fashion. For these product classes, we develop models to calculate the optimal bundle prices, order quantities, and profits under bundling. We use this analysis to establish conditions and insights under which bundling is profitable. Our analysis confirms that bundling profitability depends on individual product demands, bundling costs, and the nature of the relationship between the demands of the products to be bundled. We also provide detailed numerical examples.     

A hierarchical decomposition approach to retail shelf space management and assortment decisions

Shelf management is a crucial task in retailing. Because of the large number of products found in most retail stores (sometimes more than 60?000), current shelf space management models can only solve sub-problems of the overall store optimization problem, since the size of the complete optimization problem would be prohibitively large. Consequently, an optimal allocation of store shelf space to products has not yet been achieved. We show that a hierarchical decomposition technique, consisting of two interwoven models, is suitable to overcome this limitation and, thus, is capable of finding accurate solutions to very large and complex shelf space management problems. We further conclude that other important variables (such as product-price) can be included into the methodology and their optimal values can be determined using the same solution technique. Our methodology is illustrated on a real-life application where we predict a 22.33% increase in store profits if our model's solution is implemented.     

An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers

Three related problems arising in retail facilities with front room and back room operations, and cross-trained workers, are considered. In the first problem, the goal is to determine an optimal policy for switching workers between the two rooms. In the second and third problems, the goal is to determine the minimum number of workers that should be hired by the facility such that a satisfactory switching policy exists. We analyze two questions arising from previous work on these problems. Firstly, we demonstrate that the previously proposed policy definition is sub-optimal and cannot represent a set of solutions that are reasonable in practice, and propose an alternative definition. Secondly, we examine the problem of finding the optimal combination of cross-trained and specialized workers under a complete set of assumptions regarding worker costs. This analysis shows that the structure of the optimal solution depends on the policy definition that is employed. Moreover, under some assumptions the cost of the ‘optimal’ solution with the original policy definition will be greater than the cost of the optimal solution with the new one.     

产能约束对闭环供应链回收渠道选择的影响

在制造商存在产能约束下,建立了再制造闭环供应链回收渠道决策的Stackelberg博弈模型,得出了三种回收渠道下的回收率、零售价以及制造商、零售商和供应链的利润,分析了制造商的生产能力对回收渠道决策的影响。研究表明:存在产能约束时,制造商回收渠道中的回收率总是最高的,这与无产能约束时零售商回收渠道中回收率最高的情况明显不同;同时,若废旧产品回收转移支付价格较低,制造商会选择自己回收,此时的零售价最低,制造商、零售商和供应链利润最高;若回收转移支付价格较高,制造商会选择零售商回收,此时的零售价最低,制造商和供应链利润最高。