Developing analytical distributions for temperature indices for the purposes of pricing temperature-based weather derivatives

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If deviations of daily temperature from its expected value is modelled as an Ornstein-Uhlenbeck process with time-varying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records is a particulary poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.Weather Derivatives, Temperature Models, Cooling Degree Days, Maximum Likelihood Estimation, Distribution for Correlated Variables

Estimating the Payoffs of Temperature-based Weather Derivatives

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper argues that a more direct and parsimonious approach is to model the time-series behaviour of the index itself, provided a sufficiently rich supply of historical data is available. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is assembled. The data is then used to compare the actual payoffs of temperature-based European call options with the expected payoffs computed from historical temperature records and two time-series approaches. It is concluded that expected payoffs computed directly from historical records perform poorly by comparison with the expected payoffs generated by means of competing time-series models. It is also found that modeling the relevant temperature index directly is superior to modeling average daily temperatures.Temperature, Weather Derivatives, Cooling Degree Days, Time-series Models.

The Devil is in the Detail: Hints for Practical Optimisation

Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples.gradient algorithms, unconstrained optimisation, generalised method of moments.

Discrete time-series models when counts are unobservable

Count data in economics have traditionally been modeled by means of integer-valued autoregressive models. Consequently, the estimation of the parameters of these models and their asymptotic properties have been well documented in the literature. The models comprise a description of the survival of counts generally in terms of a binomial thinning process and an independent arrivals process usually specified in terms of a Poisson distribution. This paper extends the existing class of models to encompass situations in which counts are latent and all that is observed is the presence or absence of counts. This is a potentially important modification as many interesting economic phenomena may have a natural interpretation as a series of 'events' that are driven by an underlying count process which is unobserved. Arrivals of the latent counts are modeled either in terms of the Poisson distribution, where multiple counts may arrive in the sampling interval, or in terms of the Bernoulli distribution, where only one new arrival is allowed in the same sampling interval. The models with latent counts are then applied in two practical illustrations, namely, modeling volatility in financial markets as a function of unobservable 'news' and abnormal price spikes in electricity markets being driven by latent 'stress'.Integer-valued autoregression, Poisson distribution, Bernoulli distribution, latent factors, maximum likelihood estimation

Differential Effects of Buffer pH On Ca\u3csup\u3e2+\u3c/sup\u3e-Induced ROS Emission with Inhibited Mitochondrial Complexes I and III

Excessive mitochondrial reactive oxygen species (ROS) emission is a critical component in the etiology of ischemic injury. Complex I and complex III of the electron transport chain are considered the primary sources of ROS emission during cardiac ischemia and reperfusion (IR) injury. Several factors modulate ischemic ROS emission, such as an increase in extra-matrix Ca2+, a decrease in extra-matrix pH, and a change in substrate utilization. Here we examined the combined effects of these factors on ROS emission from respiratory complexes I and III under conditions of simulated IR injury. Guinea pig heart mitochondria were suspended in experimental buffer at a given pH and incubated with or without CaCl2. Mitochondria were then treated with either pyruvate, a complex I substrate, followed by rotenone, a complex I inhibitor, or succinate, a complex II substrate, followed by antimycin A, a complex III inhibitor. H2O2 release rate and matrix volume were compared with and without adding CaCl2 and at pH 7.15, 6.9, or 6.5 with pyruvate + rotenone or succinate + antimycin A to simulate conditions that may occur during in vivo cardiac IR injury. We found a large increase in H2O2 release with high [CaCl2] and pyruvate + rotenone at pH 6.9, but not at pHs 7.15 or 6.5. Large increases in H2O2 release rate also occurred at each pH with high [CaCl2] and succinate + antimycin A, with the highest levels observed at pH 7.15. The increases in H2O2 release were associated with significant mitochondrial swelling, and both H2O2 release and swelling were abolished by cyclosporine A, a desensitizer of the mitochondrial permeability transition pore (mPTP). These results indicate that ROS production by complex I and by complex III is differently affected by buffer pH and Ca2+ loading with mPTP opening. The study suggests that changes in the levels of cytosolic Ca2+ and pH during IR alter the relative amounts of ROS produced at mitochondrial respiratory complex I and complex III

“If You Are Old Enough to Die for Your Country, You Should Be Able to Get a Pinch of Snuff”: Views of Tobacco 21 Among Appalachian Youth

Background: Multiple strategies have been utilized in attempts to decrease the prevalence of youth tobacco use. One strategy, raising the minimum legal sale age (MLSA) of tobacco products to 21, known as Tobacco 21, has recently gained popularity. Tobacco 21 legislation targets youth tobacco use by obstructing two main sources of youth tobacco products: stores and older friends. Although these sources are the most common for youth across the nation, regional differences have not been explored. Further, youth perspectives about raising the tobacco MLSA have not been considered. Youth may help identify potential challenges to implementing tobacco control measures, as well as suggest alternatives for intervention, thus helping to shape successful tobacco control policies. Study Aim: This study aimed to 1) examine youth perspectives on raising the tobacco minimum legal sale age to 21 and 2) identify common sources of tobacco products among middle and high school students living in rural, low-income Appalachian communities. Methods: A cross-sectional survey about perceptions and use of tobacco products was conducted with students in the Appalachian regions of Kentucky and North Carolina (N=426). Questions were asked concerning perspectives on the effect of Tobacco 21 implementation. Descriptive statistics characterized participants by Tobacco 21 perspectives. Participants were given the opportunity to further expand upon their opinions in an open-ended format. Results: The majority (58.7%) of participants responded that the same number of youth would use tobacco if the legal purchase age were raised, followed by responses that fewer would use (28.9%) and more would use (12.4%). Significant differences emerged based on tobacco use status (p\u3c.05), friends’ tobacco use (p\u3c.001), and whether participants identified family members as sources of youth tobacco products (p=.047). When given the opportunity to expand upon their views concerning the implementation of Tobacco 21 laws in their communities, many respondents cited poor enforcement of tobacco MLSAs at stores, continued access to tobacco products from family members and friends, and the overall abundance of tobacco in their communities as potential barriers to the successful implementation. Conclusion: Fewer than one-third of participants believed that Tobacco 21 legislation would succeed in reducing the prevalence of youth tobacco use. Perspectives on the effect of Tobacco 21 legislation were related to personal tobacco use, exposure to tobacco users, and beliefs that family members provide tobacco products to youth. Open-ended responses identify potential obstacles in implementing Tobacco 21 legislation in Appalachia. Future research should attempt to include youth perspectives when designing and implementing tobacco control policies and examine family members as sources of tobacco products for youth

Impact of sea ice on the marine iron cycle and phytoplankton productivity

Iron is a key nutrient for phytoplankton growth in the surface ocean. At high latitudes, the iron cycle is closely related to the dynamics of sea ice. In recent decades, Arctic sea ice cover has been declining rapidly and Antarctic sea ice has exhibited large regional trends. A significant reduction of sea ice in both hemispheres is projected in future climate scenarios. In order to adequately study the effect of sea ice on the polar iron cycle, sea ice bearing iron was incorporated in the Community Earth System Model (CESM). Sea ice acts as a reservoir for iron during winter and releases the trace metal to the surface ocean in spring and summer. Simulated iron concentrations in sea ice generally agree with observations in regions where iron concentrations are relatively low. The maximum iron concentrations simulated in Arctic and Antarctic sea ice are much lower than observed, which is likely due to underestimation of iron inputs to sea ice or missing mechanisms. The largest iron source to sea ice is suspended sediments, contributing fluxes of iron of 2.2 × 108 mol Fe month−1 in the Arctic and 4.1 × 106 mol Fe month−1 in the Southern Ocean during summer. As a result of the iron flux from ice, iron concentrations increase significantly in the Arctic. Iron released from melting ice increases phytoplankton production in spring and summer and shifts phytoplankton community composition in the Southern Ocean. Results for the period of 1998 to 2007 indicate that a reduction of sea ice in the Southern Ocean will have a negative influence on phytoplankton production. Iron transport by sea ice appears to be an important process bringing iron to the central Arctic. The impact of ice to ocean iron fluxes on marine ecosystems is negligible in the current Arctic Ocean, as iron is not typically the growth-limiting nutrient. However, it may become a more important factor in the future, particularly in the central Arctic, as iron concentrations will decrease with declining sea ice cover and transport

N-15-Rich Organic Globules in a Cluster IDP and the Bells CM2 Chondrite

Organic matter in primitive meteorites and chondritic porous interplanetary dust particles (CP IDPs) is commonly enriched in D/H and 15N/14N relative to terrestrial values [1-3]. These anomalies are ascribed to the partial preservation of presolar cold molecular cloud material [1]. Some meteorites and IDPs contain m-size inclusions with extreme H and N isotopic anomalies [2-4], possibly due to preserved pristine primordial organic grains. We recently showed that the in the Tagish Lake meteorite, the principle carriers of these anomalies are sub- m, hollow organic globules [5]. The globules likely formed by photochemical processing of organic ices in a cold molecular cloud or the outermost regions of the protosolar disk [5]. We proposed that similar materials should be common among primitive meteorites, IDPs, and comets. Similar objects have been observed in organic extracts of carbonaceous chondrites [6-8], however their N and H isotopic compositions are generally unknown. Bulk H and N isotopic compositions may indicate which meteorites best preserve interstellar organic compounds. Thus, we selected the Bells CM2 carbonaceous chondrites for study based on its large bulk 15N (+335 %) and D (+990 %) [9]