Analytic approximations for multi-asset option pricing

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi- or single-asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi-asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single-asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi-asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi-asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi-asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.

Decision making for HVAC&R system selection for a typical office building in the UK

Demands for thermal comfort, better indoor air quality together with lower environmental impacts have had ascending trends in the last decade. In many circumstances, these demands could not be fully covered through the soft approach of bioclimatic design like optimisation of the building orientation and internal layout. This is mostly because of the dense urban environment and building internal energy loads. In such cases, heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems make a key role to fulfill the requirements of indoor environment. Therefore, it is required to select the most proper HVAC&R system. In this study, a robust decision making approach for HVAC&R system selection is proposed. Technical performance, economic aspect and environmental impacts of 36 permutations of primary and secondary systems are taken into account to choose the most proper HVAC&R system for a case study office building. The building is a representative for the dominant form of office buildings in the UK. Dynamic performance evaluation of HVAC&R alternatives using TRNSYS package together with life cycle energy cost analysis provides a reliable basis for decision making. Six scenarios broadly cover the decision makers' attitudes on HVAC&R system selection which are analysed through Analytical Hierarchy Process (AHP). One of the significant outcomes reveals that, despite both the higher energy demand and more investment requirements associated with compound heating, cooling and power system (CCHP); this system is one of the top ranked alternatives due to the lower energy cost and C02 emissions. The sensitivity analysis reveals that in all six scenarios, the first five top ranked alternatives are not changed. Finally, the proposed approach and the results could be used by researchers and designers especially in the early stages of a design process in which all involved bodies face the lack of time, information and tools for evaluation of a variety of systems.

Analytic Benchmark Solutions for Open-Channel Flows

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Effects of psychotherapy for anxiety in children and adolescents: a meta-analytic review

This paper provides a comprehensive quantitative review of high quality randomized controlled trials of psychological therapies for anxiety disorders in children and young people. Using a systematic search for randomized controlled trials which included a control condition and reported data suitable for meta-analysis, 55 studies were included. Eligible studies were rated for methodological quality and outcome data were extracted and analyzed using standard methods. Trial quality was variable, many studies were underpowered and adverse effects were rarely assessed; however, quality ratings were higher for more recently published studies. Most trials evaluated cognitive behavior therapy or behavior therapy and most recruited both children and adolescents. Psychological therapy for anxiety in children and young people was moderately effective overall, but effect sizes were small to medium when psychological therapy was compared to an active control condition. The effect size for non-CBT interventions was not significant. Parental involvement in therapy was not associated with differential effectiveness. Treatment targeted at specific anxiety disorders, individual psychotherapy, and psychotherapy with older children and adolescents had effect sizes which were larger than effect sizes for treatments targeting a range of anxiety disorders, group psychotherapy, and psychotherapy with younger children. Few studies included an effective follow-up. Future studies should follow CONSORT reporting standards, be adequately powered, and assess follow-up. Research trials are unlikely to address all important clinical questions around treatment delivery. Thus, careful assessment and formulation will remain an essential part of successful psychological treatment for anxiety in children and young people.

Investigating global tropical cyclone activity with a hierarchy of AGCMs: the role of model resolution

The ability to run General Circulation Models (GCMs) at ever-higher horizontal resolutions has meant that tropical cyclone simulations are increasingly credible. A hierarchy of atmosphere-only GCMs, based on the Hadley Centre Global Environmental Model (HadGEM1), with horizontal resolution increasing from approximately 270km to 60km (at 50N), is used to systematically investigate the impact of spatial resolution on the simulation of global tropical cyclone activity, independent of model formulation. Tropical cyclones are extracted from ensemble simulations and reanalyses of comparable resolutions using a feature-tracking algorithm. Resolution is critical for simulating storm intensity and convergence to observed storm intensities is not achieved with the model hierarchy. Resolution is less critical for simulating the annual number of tropical cyclones and their geographical distribution, which are well captured at resolutions of 135km or higher, particularly for Northern Hemisphere basins. Simulating the interannual variability of storm occurrence requires resolutions of 100km or higher; however, the level of skill is basin dependent. Higher resolution GCMs are increasingly able to capture the interannual variability of the large-scale environmental conditions that contribute to tropical cyclogenesis. Different environmental factors contribute to the interannual variability of tropical cyclones in the different basins: in the North Atlantic basin the vertical wind shear, potential intensity and low-level absolute vorticity are dominant, while in the North Pacific basins mid-level relative humidity and low-level absolute vorticity are dominant. Model resolution is crucial for a realistic simulation of tropical cyclone behaviour, and high-resolution GCMs are found to be valuable tools for investigating the global location and frequency of tropical cyclones.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

The competition–performance relation: a meta-analytic review and test of the opposing processes model of competition and performance

What is the relation between competition and performance? The present research addresses this important multidisciplinary question by conducting a meta-analysis of existing empirical work and by proposing a new conceptual model—the opposing processes model of competition and performance. This model was tested by conducting an additional meta-analysis and 3 new empirical studies. The first meta-analysis revealed that there is no noteworthy relation between competition and performance. The second meta-analysis showed, in accord with the opposing processes model, that the absence of a direct effect is the result of inconsistent mediation via achievement goals: Competition prompts performance-approach goals which, in turn, facilitate performance; and competition also prompts performance-avoidance goals which, in turn, undermine performance. These same direct and mediational findings were also observed in the 3 new empirical studies (using 3 different conceptualizations of competition and attending to numerous control variables). Our findings provide both interpretational clarity regarding past research and conceptual guidance regarding future research on the competition–performance relation.

Forgetting as a consequence of retrieval: a meta-analytic review of retrieval-induced forgetting

Retrieving a subset of items can cause the forgetting of other items, a phenomenon referred to as retrieval-induced forgetting. According to some theorists, retrieval-induced forgetting is the consequence of an inhibitory mechanism that acts to reduce the accessibility of non-target items that interfere with the retrieval of target items. Other theorists argue that inhibition is unnecessary to account for retrieval-induced forgetting, contending instead that the phenomenon can be best explained by non-inhibitory mechanisms, such as strength-based competition or blocking. The current paper provides the first major meta-analysis of retrieval-induced forgetting, conducted with the primary purpose of quantitatively evaluating the multitude of findings that have been used to contrast these two theoretical viewpoints. The results largely supported inhibition accounts, but also provided some challenging evidence, with the nature of the results often varying as a function of how retrieval-induced forgetting was assessed. Implications for further research and theory development are discussed.

Letters in cognitive analytic therapy: The patient's experience

Patient perspectives on how therapeutic letters contributed to their experience of cognitive analytic therapy (CAT) were investigated. Eight patients took part in semistructured interviews. A grounded, thematic analysis of their accounts suggested four general processes. First, letters offered a tangible, lasting framework for the assimilation of a new perspective about themselves and their relationships and facilitated coping with a complex range of emotions and risks this awareness required. Second, they demonstrated therapists’ commitment to patients’ growth. Third, they helped to teach participants about the therapy process as an example of an interpersonal exchange. Fourth, they helped participants consider how they wished to share personal information. These data offer a more complex understanding of this standard CAT intervention. Although some findings are consistent with CAT theory, the range of emotional dilemmas associated with letters has not received specific attention. Clinical implications are discussed.