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.

Real option pricing in mixed-use development projects

The application of real options theory to commercial real estate has developed rapidly during the last 15 Years. In particular, several pricing models have been applied to value real options embedded in development projects. In this study we use a case study of a mixed use development scheme and identify the major implied and explicit real options available to the developer. We offer the perspective of a real market application by exploring different binomial models and the associated methods of estimating the crucial parameter of volatility. We include simple binomial lattices, quadranomial lattices and demonstrate the sensitivity of the results to the choice of inputs and method.

To what extent do pupils perceive science to be inconsistent with religious faith? An exploratory survey of 13-14 year-old English pupils

Scientists hold a wide range of beliefs on matters of religion, although popular media coverage in the UK commonly suggests that atheism is a core commitment for scientists. Considering the relationship between religion and science is a recommended topic in the English National Curriculum for lower secondary pupils (11-14 year-olds), and it is expected that different perspectives will be considered. However it is well established that many pupils may have difficulty accessing sophisticated ideas about the nature of science, and previous research suggests some may identify science with scientism. To explore pupil impressions of the relationship between science and religion, 13-14 year old pupils were surveyed in one class from each of four English secondary schools, by asking them to rate a set of statements about the relationship between science and religion, and scientific and religious perspectives on the origins of the world, and of life on earth, on the value of prayer and on the status of miracles. The survey revealed diverse views on these issues, reflecting the wider society. However it was found that a considerable proportion of the pupils in the sample considered religious beliefs and scientific perspectives to be opposed. The basis and potential consequences of such views are considered, and the need for more attention to this area of student thinking is highlighted.

Coverage-dependent molecular tilt of carbon monoxide chemisorbed on Pt{110}: A combined LEED and DFT structural analysis

The adsorption of carbon monoxide on the Pt{110} surface at coverages of 0.5 ML and 1.0 ML was investigated using quantitative low-energy electron diffraction (LEED IV) and density-functional theory (DFT). At 0.5 ML CO lifts the reconstruction of the clean surface but does not form an ordered overlayer. At the saturation coverage, 1.0 ML, a well-ordered p(2×1) superstructure with glide line symmetry is formed. It was confirmed that the CO molecules adsorb on top of the Pt atoms in the top-most substrate layer with the molecular axes tilted by ±22° with respect to the surface normal in alternating directions away from the close packed rows of Pt atoms. This is accompanied by significant lateral shifts of 0.55 Å away from the atop sites in the same direction as the tilt. The top-most substrate layer relaxes inwards by −4% with respect to the bulk-terminated atom positions, while the consecutive layers only show minor relaxations. Despite the lack of long-range order in the 0.5 ML CO layer it was possible to determine key structural parameters by LEED IV using only the intensities of the integer-order spots. At this coverage CO also adsorbs on atop sites with the molecular axis closer to the surface normal (b10°). The average substrate relaxations in each layer are similar for both coverages and consistent with DFT calculations performed for a variety of ordered structures with coverages of 1.0 ML and 0.5 ML.

Predicting the annual performance of UK real estate: timeliness versus coverage

The IPD Annual Index is the largest and most comprehensive Real Estate market index available in the UK Such coverage however inevitably leads to delays in publication. In contrast there are a number of quarterly and monthly indices which are published within days of the year end but which lack the coverage in terms of size and numbers of properties. This paper analyses these smaller but more timely indices to see whether such indices can be used to predict the performance of the IPD Annual Index. Using a number of measures of forecasting accuracy it is shown that the smaller indices provide unbiased and efficient predictions of the IPD Annual Index. Such indices also significantly outperform a naive no-change model. Although no one index performs significantly better than the others. The more timely indices however do not perfectly track the IPD Annual Index. As a result any short run predictions of performance will be subject to a degree of error. Nevertheless the more timely indices, although lacking authoritative coverage, provide a valuable service to investors giving good estimates of Real Estates performance well before the publication of the IPD Annual Index.

Use of batch culture and a two-stage continuous culture system to study the effect of supplemental a-lactalbumin and glycomacropeptide on mixed populations of human gut bacteria

Certain milk factors can promote the growth of a host-friendly gastrointestinal microflora. This may explain why breast-fed infants experience fewer intestinal infections than their formula-fed counterparts. The effect of formula supplementation with two such factors was investigated in this study. Infant faecal specimens were used to ferment formulas supplemented with glycomacropeptide and α-lactalbumin in a two-stage compound continuous culture model. Bacteriology was determined by fluorescence in situ hybridisation. Vessels that contained breast milk as well as α-lactalbumin and glycomacropeptide had stable counts of bifidobacteria while lactobacilli increased significantly only in vessels with breast milk. Bacteroides, clostridia and Escherichia coli decreased significantly in all runs. Acetate was the principal acid found along with high amounts of propionate and lactate. Supplementation of infant formulas with appropriate milk proteins may be useful in simulating the beneficial bacteriological effects of breast milk.

The influence of plant species number on productivity, ground coverage and floral performance in grass-free lawns

The grass-free lawn is a novel development in modern ornamental horticulture where the traditional monoculture of grass is replaced by a variety of mowing-tolerant clonal forbs. It brings floral aesthetics and a diverse species approach to the use of lawn space. How the number of constituent forb species affects the aesthetic and structural performance of grass-free lawns was investigated using grass-free lawns composed of four, six and twelve British native clonal perennial forb species. Lawn productivity was seen to increase with increasing species number but the relationship was not linear. Plant cover was dynamic in all lawn types, varied between years and was not representative of individual species' floral performance. The behaviour of component species common to all lawns suggested that lawns with 12 species show greater structural stability than the lawns with a lower species number. Visual performance in lawns with the greatest species number was lower than in lawns with fewer species, with increasing variety in floral size and individual species floral productivity leading to a trade-off between diversity and floral performance. Individual species were seen to have different aesthetic functions in grass-free lawns either by providing flowers, ground coverage or both.

The bi-cultural option for international human resource management: the Japanese/Brazilian Nikkeijin example

This paper reports on an important subgroup of international boundary-spanners – immigrants and second or third generation migrants from the MNC's home country living in the subsidiary host country. We take as our example the Nikkeijin (Japanese immigrants and their descendants) in Brazil. Such bi-cultural people are a largely unexplored source of boundary-spanning internationally competent talent for multinational enterprises. Using two different surveys, we find that this group is recognized as a source of talent by Japanese MNCs, but that their HRM practices are not appropriate to attract and use them in their global talent management programmes.

Coverage-dependent structural evolution in the interaction of NO2 with Au{111}

We have used low-temperature STM, together with DFT calculations incorporating the effects of dispersion forces, to study from a structural point of view the interaction of NO2 with Au{111} surfaces. NO2 adsorbs molecularly on Au{111} at 80 K, initially as small, disordered clusters at the elbows of the type-x reconstruction lines of the clean-surface herringbone reconstruction, and then as larger, ordered islands on the fcc regions. Within the islands, the NO2 molecules define a (√3 × 2)rect. superlattice, for which we evaluate structural models. By around 0.25 ML coverage, the herringbone reconstruction has been lifted, accompanied by the formation of Au nanoclusters, and the islands have coalesced. At this stage, essentially the whole surface is covered with an overlayer consisting predominantly of domains of the (√3 × 2)rect. structure, but also containing less wellordered regions. With further exposure, the degree of disorder in the overlayer increases; saturation occurs close to 0.43 ML.

Sampling uncertainty in gridded sea surface temperature products and Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data

Sea surface temperature (SST) data are often provided as gridded products, typically at resolutions of order 0.05 degrees from satellite observations to reduce data volume at the request of data users and facilitate comparison against other products or models. Sampling uncertainty is introduced in gridded products where the full surface area of the ocean within a grid cell cannot be fully observed because of cloud cover. In this paper we parameterise uncertainties in SST as a function of the percentage of clear-sky pixels available and the SST variability in that subsample. This parameterisation is developed from Advanced Along Track Scanning Radiometer (AATSR) data, but is applicable to all gridded L3U SST products at resolutions of 0.05-0.1 degrees, irrespective of instrument and retrieval algorithm, provided that instrument noise propagated into the SST is accounted for. We also calculate the sampling uncertainty of ~0.04 K in Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) products, using related methods.

The option market reaction to bank loan announcements

In this study, we examine the options market reaction to bank loan announcements for the population of US firms with traded options and loan announcements during 1996-2010. We get evidence on a significant options market reaction to bank loan announcements in terms of levels and changes in short-term implied volatility and its term structure, and observe significant decreases in short-term implied volatility, and significant increases in the slope of its term structure as a result of loan announcements. Our findings appear to be more pronounced for firms with more information asymmetry, lower credit ratings and loans with longer maturities and higher spreads. Evidence is consistent with loan announcements providing reassurance for investors in the short-term, however, over longer time horizons, the increase in the TSIV slope indicates that investors become increasingly unsure over the potential risks of loan repayment or uses of the proceeds.

Moral uncertainty and permissibility: evaluating option sets

In this essay, we explore an issue of moral uncertainty: what we are permitted to do when we are unsure about which moral principles are correct. We develop a novel approach to this issue that incorporates important insights from previous work on moral uncertainty, while avoiding some of the difficulties that beset existing alternative approaches. Our approach is based on evaluating and choosing between option sets rather than particular conduct options. We show how our approach is particularly well-suited to address this issue of moral uncertainty with respect to agents that have credence in moral theories that are not fully consequentialist.