GENERALIZATION OF THE DYBVIG–INGERSOLL–ROSS THEOREM AND ASYMPTOTIC MINIMALITY

The long‐term limit of zero‐coupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross theorem, which says that long‐term spot and forward rates can never fall in an arbitrage‐free model. Extensions of popular interest rate models needing this generalization are presented. In addition, we discuss several definitions of arbitrage, prove asymptotic minimality of the limit superior of the spot rates, and illustrate our results by several continuous‐time short‐rate models.     

A two‐mean reverting‐factor model of the term structure of interest rates

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference) between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor (Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities. However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data, and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003     

Small‐cost asymptotics for long‐term growth rates in incomplete markets

This paper provides a rigorous asymptotic analysis of long‐term growth rates under both proportional and Morton–Pliska transaction costs. We consider a general incomplete financial market with an unspanned Markov factor process that includes the Heston stochastic volatility model and the Kim–Omberg stochastic excess return model as special cases. Using a dynamic programming approach, we determine the leading‐order expansions of long‐term growth rates and explicitly construct strategies that are optimal at the leading order. We further analyze the asymptotic performance of Morton–Pliska strategies in settings with proportional transaction costs. We find that the performance of the optimal Morton–Pliska strategy is the same as that of the optimal one with costs increased by a factor of . Finally, we demonstrate that our strategies are in fact pathwise optimal, in the sense that they maximize the long‐run growth rate path by path.     

Monetary policy and long‐term interest rates: Evidence from the U.S. economy

This paper addresses the ability of central banks to affect the structure of interest rates. We assess the causal relationship between the short‐term Effective Federal Funds Rate (FF) and long‐term interest rates associated with both public and private bonds and specifically, the 10‐Year Treasury Bond (GB10Y) and the Moody's Aaa Corporate Bond (AAA). To do this, we apply Structural Vector Autoregressive models to U.S. monthly data for the 1954–2018 period. Based on results derived from impulse response functions and forecast error variance decomposition, we find: a bidirectional relationship when GB10Y is considered as the long‐term rate and a unidirectional relationship that moves from short‐ to long‐term interest rates when AAA is considered. These conclusions show that monetary policy is able to permanently affect long‐term interest rates and the central bank has a certain degree of freedom in setting the levels of the short‐term policy rate.     

A Reconsideration of Rent‐to‐Own

Rent‐to‐own agreements (RTO) are traditionally seen as disguised installment contracts imposed on uninformed consumers at usurious interest rates. After the flaws and omissions in these interest rate calculations are addressed, the implied annual percentage rates (APRs) remain extraordinarily high. It is shown that alternatives to RTO, such as layaway and long‐term rental, yield comparable APRs. The appeal of rent‐to‐own is then attributed to its structure that includes an initial pure rental phase of high value to persons in volatile financial and/or personal situations followed by an installment phase. Should these situations be resolved, the consumer exercises an imbedded option to acquire a perhaps otherwise unobtainable installment agreement at a competitive interest rate.     

A two‐sector neo‐Kaleckian model of growth and distribution: Investment allocation and evolutionary dynamics

This paper focuses on the two‐sector neo‐Kaleckian model of growth and distribution that was developed by Dutt (1990) and challenged by Park (1995). We develop a variant of this model, focusing on the supply‐side to solve the overdetermination problem that was raised by Park. Finally, we introduce evolutionary dynamics to model the investment flows between the capital and consumer goods sectors. In this setup, the sectoral profit rates and the size of capital stocks wield an essential role upon the entrepreneur’s decision on which sector to invest in. This model is perfectly determined and it generates a stable evolutionary equilibrium over the long term.     

Self‐similarity in long‐horizon returns

Asset returns incorporate new information via the effects of independent and possibly identically distributed random shocks. They may also incorporate long memory effects related to the concept of self‐similarity. The two approaches are here combined. In addition, methods are proposed for estimating the contribution of each component and evidence supporting the presence of both components in both the physical and risk‐neutral distributions is presented. Furthermore, it is shown that long‐horizon returns may be nonnormal when there is a self‐similar component. The presence of a self‐similar component also questions positive equity biases over the longer term.     

Long‐term information,short‐lived securities

The authors explore strategic trade in short‐lived securities by agents who have private information that is potentially long‐term, but do not know how long their information will remain private. Trading short‐lived securities is profitable only if enough of the private information becomes public prior to contract expiration; otherwise the security will worthlessly expire. How this results in trading behavior fundamentally different from that observed in standard models of informed trading in equity is highlighted. Specifically, it is shown that informed speculators are more reluctant to trade shorter‐term securities too far in advance of when their information will necessarily be made public, and that existing positions in a shorter‐term security make future purchases more attractive. Because informed speculators prefer longer‐term securities, this can make trading shorter‐term contracts more attractive for liquidity traders. The conditions are characterized under which liquidity traders choose to incur extra costs to roll over short‐term positions rather than trade in distant contracts, providing an explanation for why most longer‐term derivative security markets have little liquidity and large bid‐ask spreads. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:465–502, 2006     

On the relation between linearity‐generating processes and linear‐rational models

We review the notion of a linearity‐generating (LG) process introduced by Gabaix and relate LG processes to linear‐rational (LR) models studied by Filipovi? et al. We show that every LR model can be represented as an LG process and vice versa. We find that LR models have two basic properties that make them an important representation of LG processes. First, LR models can be easily specified and made consistent with nonnegative interest rates. Second, LR models go naturally with the long‐term risk factorization due to Alvarez and Jermann, Hansen and Scheinkman, and Qin and Linetsky. Every LG process under the long forward measure can be represented as a lower dimensional LR model.     

SOCIAL DISCOUNTING AND THE LONG RATE OF INTEREST

The well‐known theorem of Dybvig, Ingersoll, and Ross shows that the long zero‐coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long‐term discount function has an exponential tail. We revisit the problem in the setting of modern interest rate theory, and show that if the long “simple” interest rate (or Libor rate) is finite, then this rate (unlike the zero‐coupon rate) acts viably as a state variable, the value of which can fluctuate randomly in line with other economic indicators. New interest rate models are constructed, under this hypothesis and certain generalizations thereof, that illustrate explicitly the good asymptotic behavior of the resulting discount bond systems. The conditions necessary for the existence of such “hyperbolic” and “generalized hyperbolic” long rates are those of so‐called social discounting, which allow for long‐term cash flows to be treated as broadly “just as important” as those of the short or medium term. As a consequence, we are able to provide a consistent arbitrage‐free valuation framework for the cost‐benefit analysis and risk management of long‐term social projects, such as those associated with sustainable energy, resource conservation, and climate change.     

Disaster Resilience Through Public–Private Short‐Term Collaboration

While contingency planning may provide a perspective for anticipating critical incidents, supply chain managers must develop competencies to address the long‐term disruptions that stem from both natural and man‐made disasters. The broad‐reaching nature of disasters brings public and private entities together and often requires collaboration to revitalize disrupted supply chains. Leveraging supply chain governance logic through the dual lenses of resource management and competing values, a research framework is introduced to address the nature of public–private short‐term collaboration and its influence on supply chain resilience. The largely unstudied concept of short‐term collaboration is at the heart of a model focusing on the alignment and adjustment of potentially disparate organizational values (public/private) to establish collective responsiveness while facilitating the fulfillment of mutual goals for a single event and/or discrete repeat events. We offer research propositions pertaining to the model and conclude with a discussion of managerial implications and the dire need for future research.     

The IMF After the Asian Crisis: Merits and Limitations of the ‘Long‐term Development Partner’ Role

We examine the view, espoused by a number of commentators in recent months, that the International Monetary Fund (IMF) should seek to withdraw from its long‐term lending operations, in the wake of the recent financial crisis in Asia and elsewhere, and restrict itself to its ‘core competency’ of preventing and where necessary lending into financial crisis. This view is based on a belief that such long‐term lending crowds out both private sector operations and short‐term IMF lending; and that it is ineffective, because of weaknesses in the IMF’s conditionality. Both of these propositions, we argue, can be challenged. In the poorer developing countries there is virtually no private sector to crowd out, and Enhanced Structural Adjustment Facility (ESAF) operations have been conspicuously successful, not only at promoting growth, but also at achieving structural changes not at all achieved by aid donors such as strengthening the tax base. Such changes inevitably require a longer time‐period than the standard three years of an IMF standby, not only in order to induce a production response but also in order to achieve the necessary measure of stabilisation and economic reform without imposing social pressures which wreck the production response. The latter argument is particularly powerful in middle income countries, and provides an argument for IMF support to these countries also whilst they are temporarily excluded from international capital markets. Often also a long‐term presence is needed to achieve effective leverage in short‐term operations. In such cases the IMF’s long‐term lending should be seen as preconditional to the success of, and not as an alternative to, its short‐term operations. We therefore argue for the retention of the Fund’s long‐term lending function; and for this function not to be transferred to the World Bank, which has less credibility in global financial markets and less comparative advantage in macro‐economic management. Measures are indeed needed to reduce the level of the IMF’s exposure to risk in poorer developing countries, but those, we believe, should consist of the preventive measures currently going on, and measures to increase the ratio of equity to debt, rather than measures which would jeopardise the progress in long‐term poverty alleviation capacity achieved by the Fund over recent years     

Long‐Term Orientation and Commitment in Export Joint Ventures among Small and Medium‐Sized Firms

Alliances may be an important tool for overcoming the resource and capability deficiencies facing small and medium‐sized enterprises (SMEs), as they help strengthen their market position and facilitate access to new markets. In this paper we focus on domestic joint ventures (JVs) for export purposes. Our aim is to analyze the influence of partners' long‐term orientation on their commitment, while looking into the key antecedents of long‐term orientation: complementarity of partners' resources and trust. The hypotheses set forth are tested on a sample of 70 Spanish domestic export JVs. The data were analyzed using partial least squares (PLS) analysis. Our paper contributes to the literature on export JVs and SMEs by providing evidence that long‐term orientation reinforces commitment to devoting the necessary resources and efforts to enable the export JV to succeed. The results also indicate that trust decisively determines the long‐term orientation of the partners to an export JV, and that complementarity of resources plays a relevant role in the development of long‐term orientation by facilitating trust.     

On the Link Between Exchange‐rate Regimes,Capital Controls and Monetary Policy Autonomy in Small European Countries, 1979–2000

We investigate international monetary‐policy transmission under different exchange‐rate and capital‐account regimes in eleven small, open economies during the 1980s and 1990s. We find no systematic link between ex‐post monetary‐policy autonomy and exchange‐rate regimes. Capital controls appear to have provided a degree of temporal insulation from foreign monetary policy shocks, though not strict autonomy. The results are consistent both with short‐term autonomy for small countries even under fixed exchange rates and an open capital account, and with long‐term dependence under flexible exchange rates and an independent stability target. Results also indicate that euro‐area market interest rates are significantly more responsive to the development of the corresponding US rate than were the previous national rates.     

Business Forecasting of Double‐trend Time Series: An Improved PLS‐based Time‐varying Weight Combination Approach

Business forecasting with double‐trend time series (long‐term trends and seasonal volatility) has been challenging due to its complexity. Neither a single time series model nor a fixed‐weight combination approach can fully capture the comprehensive information. We address this issue by proposing an improved partial least squares (PLS) based time‐varying weight combination approach. The proposed method can handle the relations both between the single models involved and between single models and time ordering with time‐varying weights. The test on 20 simulated datasets demonstrates the better and more robust performance of the method. We also apply it to three real datasets. The results show that our approach represents a significant improvement over the existing methods in terms of data fitness and prediction accuracy. Copyright © 2017 ASAC. Published by John Wiley & Sons, Ltd.     

Long‐term Effects of the Efficiency Wage Hypothesis in Goodwin‐type Economies

The existence of an efficiency wage mechanism in Goodwin‐type models may lead to the unexpected appearance of an economically meaningful equilibrium with zero labour share, which is globally stable for some parameter constellation and allows the system to attain its ‘maximal growth'. A subsequent ‘normative’ comparison between the possible long‐term regimes of the economy shows that (1) the zero labour share equilibrium can be the ‘preferred’ equilibrium in terms of welfare; (2) in all the long‐term regimes the welfare is higher than in the original Goodwin model; (3) a point of maximal welfare exists. Moreover, the effects of rational behaviour of firms are compared with the ‘traditional’ situation in which rationality is not explicitly assumed. A striking result appears: myopic rationality can have deleterious effects on the profit of firms and on the overall welfare of the economy.     

MULTIDIMENSIONAL DYNAMIC RISK MEASURE VIA CONDITIONAL g‐EXPECTATION

This paper deals with multidimensional dynamic risk measures induced by conditional g‐expectations. A notion of multidimensional g‐expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem, and viability on a rectangle of solutions to multidimensional backward stochastic differential equations, some necessary and sufficient conditions are given for the constancy, monotonicity, positivity, and translatability properties of multidimensional conditional g‐expectations and multidimensional dynamic risk measures; we prove that a multidimensional dynamic g‐risk measure is nonincreasingly convex if and only if the generator g satisfies a quasi‐monotone increasingly convex condition. A general dual representation is given for the multidimensional dynamic convex g‐risk measure in which the penalty term is expressed more precisely. It is shown that model uncertainty leads to the convexity of risk measures. As to applications, we show how this multidimensional approach can be applied to measure the insolvency risk of a firm with interacting subsidiaries; optimal risk sharing for ‐tolerant g‐risk measures, and risk contribution for coherent g‐risk measures are investigated. Insurance g‐risk measure and other ways to induce g‐risk measures are also studied at the end of the paper.     

HIGH‐ORDER SHORT‐TIME EXPANSIONS FOR ATM OPTION PRICES OF EXPONENTIAL LÉVY MODELS

The short‐time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In this work, a novel second‐order approximation for at‐the‐money (ATM) option prices is derived for a large class of exponential Lévy models with or without Brownian component. The results hereafter shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration. In the presence of a Brownian component, the second‐order term, in time‐t, is of the form , with d₂ only depending on Y, the degree of jump activity, on σ, the volatility of the continuous component, and on an additional parameter controlling the intensity of the “small” jumps (regardless of their signs). This extends the well‐known result that the leading first‐order term is . In contrast, under a pure‐jump model, the dependence on Y and on the separate intensities of negative and positive small jumps are already reflected in the leading term, which is of the form . The second‐order term is shown to be of the form and, therefore, its order of decay turns out to be independent of Y. The asymptotic behavior of the corresponding Black–Scholes implied volatilities is also addressed. Our method of proof is based on an integral representation of the option price involving the tail probability of the log‐return process under the share measure and a suitable change of probability measure under which the pure‐jump component of the log‐return process becomes a Y‐stable process. Our approach is sufficiently general to cover a wide class of Lévy processes, which satisfy the latter property and whose Lévy density can be closely approximated by a stable density near the origin. Our numerical results show that the first‐order term typically exhibits rather poor performance and that the second‐order term can significantly improve the approximation's accuracy, particularly in the absence of a Brownian component.     

Dynamic Arbitrage‐Free Asset Pricing with Proportional Transaction Costs

This paper studies multiperiod asset pricing theory in arbitrage‐free financial markets with proportional transaction costs. The mathematical formulation is based on a Euclidean space for weakly arbitrage‐free security markets and strongly arbitrage‐free security markets. We establish the weakly arbitrage‐free pricing theorem and the strongly arbitrage‐free pricing theorem.     

NO‐ARBITRAGE IN A NUMÉRAIRE‐INDEPENDENT MODELING FRAMEWORK

The classic approach to modeling financial markets consists of four steps. First, one fixes a currency unit. Second, one describes in that unit the evolution of financial assets by a stochastic process. Third, one chooses in that unit a numéraire, usually the price process of a positive asset. Fourth, one divides the original price process by the numéraire and considers the class of admissible strategies for trading. This approach has one fundamental drawback: Almost all concepts, definitions, and results, including no‐arbitrage conditions like NA, NFLVR, and NUPBR depend by their very definition, at least formally, on initial choices of a currency unit and a numéraire. In this paper, we develop a new framework for modeling financial markets, which is not based on ex‐ante choices of a currency unit and a numéraire. In particular, we introduce a “numéraire‐independent” notion of no‐arbitrage and derive its dual characterization. This yields a numéraire‐independent version of the fundamental theorem of asset pricing (FTAP). We also explain how the classic approach and other recent approaches to modeling financial markets and studying no‐arbitrage can be embedded in our framework.