An extreme value theory approach to calculating minimum capital risk requirements

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semiparametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.

Eliciting consumer preferences for certified animal-friendly foods: can elements of the theory of planned behavior improve choice experiment analysis?

Models used in neoclassical economics assume human behaviour to be purely rational. On the other hand, models adopted in social and behavioural psychology are founded on the ‘black box’ of human cognition. In view of these observations, this paper aims at bridging this gap by introducing psychological constructs in the well established microeconomic framework of choice behaviour based on random utility theory. In particular, it combines constructs developed employing Ajzen’s theory of planned behaviour with Lancaster’s theory of consumer demand for product characteristics to explain stated preferences over certified animal-friendly foods. To reach this objective a web survey was administered in the largest five EU-25 countries: France, Germany, Italy, Spain and the UK. Findings identify some salient cross-cultural differences between northern and southern Europe and suggest that psychological constructs developed using the Ajzen model are useful in explaining heterogeneity of preferences. Implications for policy makers and marketers involved with certified animal-friendly foods are discussed.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Relaxing the Tropics to an ‘observed’ state: analysis using a simple baroclinic model

The technique of relaxation of the tropical atmosphere towards an analysis in a month-season forecast model has previously been successfully exploited in a number of contexts. Here it is shown that when tropical relaxation is used to investigate the possible origin of the observed anomalies in June–July 2007, a simple dynamical model is able to reproduce the observed component of the pattern of anomalies given by an ensemble of ECMWF forecast runs. Following this result, the simple model is used for a range of experiments on time-scales of relaxation, variables and regions relaxed based on a control model run with equatorial heating in a zonal flow. A theory based on scale analysis for the large-scale tropics is used to interpret the results. Typical relationships between scales are determined from the basic equations, and for a specified diabatic heating a chain of deductions for determining the dependent variables is derived. Different critical time-scales are found for tropical relaxation of different dependent variables to be effective. Vorticity has the longest critical time-scale, typically 1.2 days. For temperature and divergence, the time-scales are 10 hours and 3 hours, respectively. However not all the tropical fields, in particular the vertical motion, are reproduced correctly by the model unless divergence is heavily damped. To obtain the correct extra-tropical fields, it is crucial to have the correct rotational flow in the subtropics to initiate the Rossby wave propagation from there. It is sufficient to relax vorticity or temperature on a time-scale comparable or less than their critical time-scales to obtain this. However if the divergent advection of vorticity is important in the Rossby Wave Source then strong relaxation of divergence is required to accurately represent the tropical forcing of Rossby waves.

Ideological dominance in recreation provision: towards a theory of Local Authority response to Compulsory Competitive Tendering in Britain

This paper considers how the delivery of public leisure services in Britain has been affected by the imposition of Compulsory Competitive Tendering (CCT) on the management of facilities. In particular, it focuses on the changing relationship between the central and local levels of government, theorising a tripartite local response to CCT, incorporating local statism, post-Fordist rejection of CCT and post- Fordist compliance with the aims of the central administration. The paper then discusses the actual implementation of CCT, relating the theorised responses to those witnessed in practice. This results in the delineation of a continuum of stances, ranging from pragmatic forms of local statism, such as the protection of the former direct labour force, to centrist attempts to combine the ethics of socialism with the mechanics of the market, to an outright rejection of state organisation and control. The paper concludes that although legitimate attempts have been made to protect local services, the outcome of the CCT process has undoubtedly been the regeneration of public leisure provision away from its service roots towards a market model of provision.

An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm

Recent research has shown that Lighthill–Ford spontaneous gravity wave generation theory, when applied to numerical model data, can help predict areas of clear-air turbulence. It is hypothesized that this is the case because spontaneously generated atmospheric gravity waves may initiate turbulence by locally modifying the stability and wind shear. As an improvement on the original research, this paper describes the creation of an ‘operational’ algorithm (ULTURB) with three modifications to the original method: (1) extending the altitude range for which the method is effective downward to the top of the boundary layer, (2) adding turbulent kinetic energy production from the environment to the locally produced turbulent kinetic energy production, and, (3) transforming turbulent kinetic energy dissipation to eddy dissipation rate, the turbulence metric becoming the worldwide ‘standard’. In a comparison of ULTURB with the original method and with the Graphical Turbulence Guidance second version (GTG2) automated procedure for forecasting mid- and upper-level aircraft turbulence ULTURB performed better for all turbulence intensities. Since ULTURB, unlike GTG2, is founded on a self-consistent dynamical theory, it may offer forecasters better insight into the causes of the clear-air turbulence and may ultimately enhance its predictability.

Estimation of systematic error in an equatorial ocean model using data assimilation

Assimilation of temperature observations into an ocean model near the equator often results in a dynamically unbalanced state with unrealistic overturning circulations. The way in which these circulations arise from systematic errors in the model or its forcing is discussed. A scheme is proposed, based on the theory of state augmentation, which uses the departures of the model state from the observations to update slowly evolving bias fields. Results are summarized from an experiment applying this bias correction scheme to an ocean general circulation model. They show that the method produces more balanced analyses and a better fit to the temperature observations.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

A theory of rational spatial agglomerations

We model the behavior of rational forward-looking agents in a spatial economy. The economic geography structure is built on Fujita et al. (1999)'s racetrack economy. Workers choose optimally what to consume at each period, as well as which spatial itinerary to follow in the geographical space. The spatial extent of the resulting agglomerations increases with the taste for variety and the expenditure share on manufactured goods, and decreases with transport costs. Because forward-looking agents anticipate the future formation of agglomerations, they are more responsive to spatial utility differentials than myopic agents. As a consequence, the emerging agglomerations are larger under perfect foresight spatial adjustments than under myopic ones.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.