Small-time asymptotics for basket options -- the bi-variate SABR model and the hyperbolic heat kernel on H3\mathbb{H}^3

We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both $\beta$ parameters equal to $1$ and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on hyperbolic space for $n=3$ combined with the Bellaiche [Bel81] heat kernel expansion and Laplace's method, and we give numerical results which corroborate our asymptotic formulae. Similar to the Black-Scholes case, we find that there is a phase transition from one "most-likely" path to two most-likely paths beyond some critical $K^*$.Comment: 24 pages, 10 figure

Asymptotic formulae for implied volatility in the Heston model

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.Comment: Presentation in Section 2 has been improved. Theorem 3.1 has been slightly generalised. Figures 2 and 3 now include the at-the-money point

Children and young people's experiences of participation in decision-making at home, in schools and in their communities

The aim of this study is to explore the extent to which children and young people, aged 7-17 and living in contemporary urban and rural Ireland, are able to participate and influence matters affecting them in their homes, schools and communities. The investigative focus of the study is shaped by Lundy’s (2007) conceptualisation of Article 12 of the UN Convention on the Rights of the Child, which focuses on space, voice, audience and influence. With this in mind, the objectives of this research are: to consider the extent to which children and young people have a voice and influence in matters affecting them at home, in their school and in the community where they live; to identify the facilitators and barriers to giving children and young people a voice and influence in matters affecting them in each of these settings; to examine the type of approaches used in each setting and identify examples of good practice; to distil key messages for consideration by parents and families, teachers, schools and communities in Ireland

Small-time asymptotics for a general local-stochastic volatility model with a jump-to-default: curvature and the heat kernel expansion

We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we use the Davies \cite{Dav88} upper bound for the heat kernel on a manifold with bounded Ricci curvature to deal with the tail integrals. If the correlation $\rho < 0$, our approach still works if the drift of the volatility takes a specific functional form and there is no local volatility component, and our results include the SABR model for $\beta=1, \rho \le 0$. \bl{For uncorrelated stochastic volatility models, our results also include a SABR-type model with $\beta=1$ and an affine mean-reverting drift, and the exponential Ornstein-Uhlenbeck model.} We later augment the model with a single jump-to-default with intensity \lm, which produces qualitatively different behaviour for the short-maturity smile; in particular, for $\rho=0$, log-moneyness $x > 0$, the implied volatility increases by \lm f(x) t +o(t) for some function $f(x)$ which blows up as $x \searrow 0$. Finally, we compare our result with the general asymptotic expansion in Lorig, Pagliarani \& Pascucci \cite{LPP15}, and we verify our results numerically for the SABR model using Monte Carlo simulation and the exact closed-form solution given in Antonov \& Spector \cite{AS12} for the case $\rho=0$.Comment: 27 pages, 2 figure

Children and Young People’s Participation in the Community in Ireland: Experiences and Issues

This paper presents the findings of research into children and young people’s experiences of participating in their communities in Ireland. Using a social and relational understanding of participation, the research found that children and young people are engaged in a wide range of activities in their communities. They are however often misunderstood in the community and have limited opportunities for participation in decisions affecting them. Despite these problems, they report positive experiences of participating in youth clubs and organisations, where their participation is supported by adults. The paper discusses the implications of these findings for research, public policy and community

Strengthening integrated research and capacity development within the Caribbean region

<p>Abstract</p> <p>Background</p> <p>The Caribbean region, like other developing regions of the world, faces significant challenges in conducting research, especially in the context of limited resource capacities and capabilities. Further, due to its diverse and multiple island states, research capacity is scattered and unevenly spread within the region. The Caribbean EcoHealth Programme (CEHP) is a research program that is structured to improve the capacity and capability of health professionals in the Caribbean region to respond in integrative and innovative ways to on-going and emerging environmental health challenges by means of multi-sectoral interventions.</p> <p>Methods</p> <p>Core parts of the CEHP’s mission are to (1) conduct collaborative research in areas that the region has identified as critical; (2) build and strengthening integrated approaches to research; and (3) develop and enhance basic research capacity within the Caribbean region.</p> <p>Fundamental to the success of the CEHP’s human and resource development mission has been its use of the Atlantis Mobile Laboratory (AML). The AML has allowed the CEHP program to move throughout the Caribbean and be able to respond to calls for specific research and capacity building opportunities.</p> <p>Results</p> <p>The CEHP’s five main research projects have generated the following results: (1) the Persistent Organic Pollutants (POPs) study has evaluated human exposures to POPs, heavy metals, pesticides, and zoonotic infections; (2) the Burden of Illness (BOI) studies have developed protocols for the testing of foodborne microorganisms, strengthen laboratory analytical capabilities, and determined the prevalence and incidence of food-borne illness; (3) the Rainwater Harvesting (RWH) study has evaluated the microbial and chemical quality of rainwater harvesting systems; (4) the Ecotoxicology Water (ETW) studies have provided much needed data on the quality of recreational and drinking water supplies, and (5) the Food Safety Training Program has developed Diploma and M.Sc Agri-Food Safety and Quality Assurance programmes.</p> <p>Conclusions</p> <p>The CEHP program provides a successful example of how a collaborative instead of researcher driven research agenda can lead to not only the generation of needed information, but also leave within the region where the research has been carried out the capacity and capabilities to continue to do so independent of outside interventions.</p

Intercomparison of Multiple UV-LIF Spectrometers using the Aerosol Challenge Simulator

Measurements of primary biological aerosol particles (PBAPs) have been conducted worldwide using ultraviolet light-induced fluorescence (UV-LIF) spectrometers. However, how these instruments detect and respond to known biological and non-biological particles, and how they compare, remains uncertain due to limited laboratory intercomparisons. Using the Defence Science and Technology Laboratory, Aerosol Challenge Simulator (ACS), controlled concentrations of biological and non-biological aerosol particles, singly or as mixtures, were produced for testing and intercomparison of multiple versions of the Wideband Integrated Bioaerosol Spectrometer (WIBS) and Multiparameter Bioaerosol Spectrometer (MBS). Although the results suggest some challenges in discriminating biological particle types across different versions of the same UV-LIF instrument, a difference in fluorescence intensity between the non-biological and biological samples could be identified for most instruments. While lower concentrations of fluorescent particles were detected by the MBS, the MBS demonstrates the potential to discriminate between pollen and other biological particles. This study presents the first published technical summary and use of the ACS for instrument intercomparisons. Within this work a clear overview of the data pre-processing is also presented, and documentation of instrument version/model numbers is suggested to assess potential instrument variations between different versions of the same instrument. Further laboratory studies sampling different particle types are suggested before use in quantifying impact on ambient classification.Peer reviewe