Closed form approximations for spread options

This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option and a corresponding approximation for each of its price, volatility and correlation hedge ratios. Our approach has many advantages over existing analytical approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur costs. Simulations quantify the accuracy of our approach; we also present an empirical application to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996, Correlation in energy markets. In: V. Kaminski (Ed.), Managing Energy Price Risk, pp. 71–78 (London: Risk Publications)), which is commonly used by traders.

Stochastic volatility jump-diffusions for European equity index dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.

'What with your grades?': Students motivation for and experience of vocational courses in further education

In this article we seek to explore the motivations for studying a vocational qualification of 40 students currently in further education. We consider student decision making, in terms of the support and guidance received, and examine the value these students place on their training, particularly with respect to their future employment. Drawing on qualitative data from 40 students we argue that a student’s sense of their educational identity is important in understanding their motivations for vocational training in the first instance as well as a lack of good careers information and guidance.

Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Manipulating resource allocation in plants

The distribution of nutrients and assimilates in different organs and tissues is in a constant state of flux throughout the growth and development of a plant. At key stages during the life cycle profound changes occur, and perhaps one of the most critical of these is during seed filling. By restricting the competition for reserves in Arabidopsis plants, the ability to manipulate seed size, seed weight, or seed content has been explored. Removal of secondary inflorescences and lateral branches resulted in a stimulation of elongation of the primary inflorescence and an increase in the distance between siliques. The pruning treatment also led to the development of longer and larger siliques that contained fewer, bigger seeds. This seems to be a consequence of a reduction in the number of ovules that develop and an increase in the fatty acid content of the seeds that mature. The data show that shoot architecture could have a substantial impact on the partitioning of reserves between vegetative and reproductive tissues and could be an important trait for selection in rapid phenotyping screens to optimize crop performance.

The role of the pod in seed development: strategies for manipulating yield

Pods play a key role in encapsulating the developing seeds and protecting them from pests and pathogens. In addition to this protective function, it has been shown that the photosynthetically active pod wall contributes assimilates and nutrients to fuel seed growth. Recent work has revealed that signals originating from the pod may also act to coordinate grain filling and regulate the reallocation of reserves from damaged seeds to those that have retained viability. In this review we consider the evidence that pods can regulate seed growth and maturation, particularly in members of the Brassicaceae family, and explore how the timing and duration of pod development might be manipulated to enhance either the quantity of crop yield or its nutritional properties.

Variability of starch-based thickened drinks for patients with dysphagia in the hospital setting

Starch-based thickening agents may be prescribed for patients with dysphagia. Thickened fluids alter variables of the swallow reflex, allowing more time for bolus manipulation without compromising airway closure. This investigation explored the variation in viscosity and physical characteristics of thickened drinks prepared in different media under laboratory conditions and compared the results with those of thickened drinks presented to dysphagic patients in one hospital. The rheological characteristics were tested on a simple plastometer and a Bohlin CVOR rheometer (Malvern Instruments, Worcestershire, UK). Samples prepared to “syrup” consistency both in the laboratory and in the hospitalwere significantly different from each other (P < 0.0001). This was also the case for samples prepared to “custard” consistency. Differences existed not only in viscosity, but drinks prepared in different media produced different rheological matrices. This signifies different viscoelastic behaviors that may effect manipulation in the mouth. From this study, preparation of thickened drinks using starch-based instant thickening powders appears to be a highly variable practice.