Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

Optimal Credit Rationing in Not-For-Profit Financial Institutions

We examine the dynamic optimization problem for not-for-profit financial institutions (NFPs) that maximize consumer surplus, not profits. We characterize the optimal dynamic policy and find that it involves credit rationing. Interest rates set by mature NFPs will typically be more favorable to customers than market rates, as any surplus is distributed in the form of interest rate subsidies, with credit rationing being required to prevent these subsidies from distorting loan volumes from their optimal levels. Rationing overcomes a fundamental problem in NFPs; it allows them to distribute the surplus without distorting the volume of activity from the efficient level.

Cost performance of Irish credit unions

There are 424 credit unions in Ireland with assets under their control of €14.3bn and a membership of 2.5m which equates to about 66% of the economically active population, the highest penetration level of any country. That said, the Irish movement sits at a critical development stage, well behind mature markets such as Canada and the US in terms of product provision, technological sophistication, fragmentation of trade bodies and regulatory environment. This study analyses relative cost efficiency or performance of Irish credit unions using the popular frontier approach which measures an entity’s efficiency relative to a frontier of best practice. Parametric techniques are utilised, with variation in inefficiency being attributed to credit union-specific factors. The stochastic cost frontier parameters and the credit-union specific parameters are simultaneously estimated to produce valid statistical inferences. The study finds that the majority of Irish credit unions are not operating at optimal levels. It further highlights the factors which drive efficiency variation across credit unions and they include technological sophistication, ‘sponsor donated’ resources, interest rate differentials and the levels of bad debt written off

Credit Unions: A Theoretical and Empirical Overview

In 2009 there were over 49,330 credit unions across 98 countries with more than 184 million members and approximately $1,354 billion in assets. There is a great diversity within the credit union movement across these countries. This reflects the various economic, historic and cultural contexts within which credit unions operate. This paper traces the evolution of the credit union movement. It examines credit union objectives, and considers issues relating to efficiency, technology adoption, product diversification, merger, failure and demutualization. The regulatory environment within which credit unions operate is also explored under the themes of interest rate regulation, common bond requirements, taxation, deposit insurance and capital regulation. The overview also considers demutualization and the costs and benefits to credit unions of altering their organizational form.

The Diffusion of Risks in Public Private Partnership Contracts

Purpose The UK government argues that the benefits of public private partnership (PPP) in delivering public infrastructure stem from: transferring risks to the private sector within a structure in which financiers put their own capital at risk; and, the performance based payment mechanism, reinforced by the due diligence requirements imposed by the lenders financing the projects (HM Treasury, 2010). Prior studies of risk in PPPs have investigated ‘what’ risks are allocated and to ‘whom’, that is to the public or the private sector. The purpose of this study is to examine ‘how’ and ‘why’ PPP risks are diffused by their financiers. Design/methodology/approach This study focuses on the financial structure of PPPs and on their financiers. Empirical evidence comes from interviews conducted with equity and debt financiers. Findings The findings show that the financial structure of the deals generates risk aversion in both debt and equity financiers and that the need to attract affordable finance leads to risk diffusion through a network of companies using various means that include contractual mitigation through insurance, performance support guarantees, interest rate swaps and inflation hedges. Because of the complexity this process generates, both procurers and suppliers need expensive expert advice. The risk aversion and diffusion and the consequent need for advice add cost to the projects impacting on the government’s economic argument for risk transfer. Limitations and implications The empirical work covers the private finance initiative (PFI) type of PPP arrangements and therefore the risk diffusion mechanisms may not be generalisable to other forms of PPP, especially those that do not involve the use of high leverage or private finance. Moreover, the scope of this research is limited to exploring the diffusion of risk in the private sector. Further research is needed on how risk is diffused in other settings and on the value for money implication of risk diffusion in PPP contracts. Originality/value The expectation inherent in PPP is that the private sector will better manage those risks allocated to it and because private capital is at risk, financiers will perform due diligence with the ultimate outcome that only viable projects will proceed. This paper presents empirical evidence that raises questions about these expectations. Key words: public private partnership, risk management, diffusion, private finance initiative, financiers

The Impact of Extension and Ecosystem Services on Smallholders’ Credit Constraint.

On formal credit markets, access to formal credit and reasonable credit terms of smallholder farmers
in rural sub-Saharan Africa is limited due to adverse selection. Financial institutions operating in
rural areas often cannot distinguish between borrowers (farmers) that are creditworthy and those that
are not, thus, allocate limited resource to agriculture to reduce credit risk. In the presence of limited business quality signaling by smallholder farmers, financial institutions shall demand for collateral and/or offer unfavorable contract terms. Moreover, agricultural productivity of rural sub-Saharan
Africa, dominated by subsistence or small-scale farmers, is also negatively impacted by the adverse
effect of climate change. A strategy that may make the farming practices of smallholder farmer’s
climate resilient and profitable may also improve smallholder farmer's access to formal credit. This
study investigates to what extent participating in ecosystem and extension services (EES) programs
signals business quality of smallholders, thus granting them credit accessibility. We collected data
on 210 smallholder farmers in 2013, comprising farmers that receive payments for ecosystem
services (PES) and farm management training from the International Small Group Tree Planting
Program (TIST) Kenya to test the aforementioned theory empirically. We use game theory,
particularly a screening and sorting model, to illustrate the prospects for farmers with EES to access
formal credit and to improve their credit terms given that they receive PES and banking services
training. Furthermore, the PES’ long term duration (10 – 30 years) generates stable cash-flow which
may be perceived as collateral substitute. Results suggest that smallholder farmers in the TIST
program were less likely to be credit constraint compared to non-TIST farmers. Distance to market,
education, livestock and farm income are factors that determine access to credit from microfinance
institutions in rural Kenya. Amongst farmers that have obtained loans, those keeping business records
enjoy more favorable formal credit conditions. These farmers were observed to pay ca. 5 percent less
interest rate in microfinance charges. For TIST farmers, this type of farm management practices may
be attributed to the banking services and other training they receive within the program. While the
availability of classical collateral (farmlands) and PES may reduce interest rate, the latter was found
to be statistically insignificant. This research underlines the importance of an effective extension
services in rural areas of developing countries and the need to improve gains from conservation
agriculture and ensuing PES. The benefits associated with EES and PES may encompass agricultural
financing.

Participation of Smallholders in Agroforestry Agri-Environmental Scheme: A lesson from the rural Mount Kenya region

The likelihood of smallholder farmers not participating in agroforestry agri-environmental schemes and payments for ecosystem services (PES) may be due to limited farmland endowment and formal credit constraints. These deficits may lead to an ‘exclusive club’ of successful farmers, which are not necessarily poor, enjoying the benefits of agri-environmental schemes and PES although agrienvironmental schemes and PES have been devised as a means of fostering rural sustainable development and improving the livelihood of poor smallholder farmers. Smallholder farmers in parts of rural Kenya continue to enroll in ‘The International Small Group Tree Planting Programme’ (TIST), an agri-environmental scheme, promoting agroforestry, carbon sequestration and conservation agriculture (CA). The question remains if these farmers are really poor? This study examines factors that determine the participation of smallholder farmers in TIST in parts of rural Kenya. We use survey data compiled in 2013 on 210 randomly selected smallholder farmers from Embu, Meru and Nanyuki communities; the sample consists of TIST and non-TIST members. A random utility model and logit regression were used to test a set of non-monetary and monetary factors that influence participation in the TIST. The utility function is conceptualized to give non-monetary factors, particularly the common medium of communication in rural areas – formal and informal – a central role. Furthermore, we investigate other factors (incl. credit accessibility and interest rate) that reveal the nature of farmers participating in TIST. The findings suggest that spread of information via formal and informal networks is a major driver of participation in the TIST program. Furthermore, variables such credit constrains, age and labour supply positively correlate with TIST participation, while for education the opposite is true. It is important to mention that these correlations, although somewhat consistent, were all found to be weak. The results indicate that participation in the TIST program is not influenced by farm size; therefore we argue that the TIST scheme is NOT an ‘exclusive club’ comprising wealthy and successful farmers. Older farmers’ being more likely to join the TIST is an argument for their long- rather than widely assumed short-term planning horizon and a new contribution to the literature. Given the importance of poverty alleviation and climate smart agriculture in developing countries, sustainable policy should strengthening the social and human capital as well as informal networks in rural areas. Extension services should effectively communicate benefits to less educated and credit constrained farmers.

Novel Generic Bounds on the Sum Rate of MIMO ZF Receivers

This paper introduces some novel upper and lower bounds on the achievable sum rate of multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receivers. The presented bounds are not only tractable but also generic since they apply for different fading models of interest, such as uncorrelated/ correlated Rayleigh fading and Ricean fading. We further formulate a new relationship between the sum rate and the first negative moment of the unordered eigenvalue of the instantaneous correlation matrix. The derived expressions are explicitly compared with some existing results on MIMO systems operating with optimal and minimum mean-squared error (MMSE) receivers. Based on our analytical results, we gain valuable insights into the implications of the model parameters, such as the number of antennas, spatial correlation and Ricean-K factor, on the sum rate of MIMO ZF receivers. © 2011 IEEE.

A quality-scalable and energy-efficient approach for spectral analysis of heart rate variability

Today there is a growing interest in the integration of health monitoring applications in portable devices necessitating the development of methods that improve the energy efficiency of such systems. In this paper, we present a systematic approach that enables energy-quality trade-offs in spectral analysis systems for bio-signals, which are useful in monitoring various health conditions as those associated with the heart-rate. To enable such trade-offs, the processed signals are expressed initially in a basis in which significant components that carry most of the relevant information can be easily distinguished from the parts that influence the output to a lesser extent. Such a classification allows the pruning of operations associated with the less significant signal components leading to power savings with minor quality loss since only less useful parts are pruned under the given requirements. To exploit the attributes of the modified spectral analysis system, thresholding rules are determined and adopted at design- and run-time, allowing the static or dynamic pruning of less-useful operations based on the accuracy and energy requirements. The proposed algorithm is implemented on a typical sensor node simulator and results show up-to 82% energy savings when static pruning is combined with voltage and frequency scaling, compared to the conventional algorithm in which such trade-offs were not available. In addition, experiments with numerous cardiac samples of various patients show that such energy savings come with a 4.9% average accuracy loss, which does not affect the system detection capability of sinus-arrhythmia which was used as a test case.