Bivariate Normal Mixture Spread Option Valuation

This paper explores the properties of a European spread option valuation method for correlated assets when the marginal distribution each asset return is assumed to be a mixture of normal distributions. In this ‘bivariate normal mixture’ (BNM) approach no-arbitrage option values are just weighted sums of different 2GBM values based on two correlated lognormal diffusions, and likewise for their sensitivities. The main advantage of this approach is that BNM option values are consistent with the volatility smiles for each asset and an implied correlation ‘frown’, both of which are often observed when spread options are priced under the 2GBM assumptions. It is simple to perform an extensive consideration of model values for varying strike, and for different asset volatility and correlation structures. We compare BNM valuations with those based on the ‘2GBM’ assumption of two correlated lognormal diffusions and explain the differences between the BNM values and the 2GBM values of spread options as a weighted sum of six second order 2GBM value sensitivities. We also investigate the BNM sensitivities and these, like the option values, can sometimes be significantly different from those obtained under the 2GBM model. Finally, we show how the correlation frown that is implied by this model is affected as we change the parameters in the bivariate normal mixture density of the asset returns.spread option, implied correlation, bivariate normal mixture density

Natural drivers of multidecadal Arctic sea ice variability over the last millennium

This is the final version. Available from Nature Research via the DOI in this record.The climate varies due to human activity, natural climate cycles, and natural events external to the climate system. Understanding the different roles played by these drivers of variability is fundamental to predicting near-term climate change and changing extremes, and to attributing observed change to anthropogenic or natural factors. Natural drivers such as large explosive volcanic eruptions or multidecadal cycles in ocean circulation occur infrequently and are therefore poorly represented within the observational record. Here we turn to the first high-latitude annually-resolved and absolutely dated marine record spanning the last millennium, and the Paleoclimate Modelling Intercomparison Project (PMIP) Phase 3 Last Millennium climate model ensemble spanning the same time period, to examine the influence of natural climate drivers on Arctic sea ice. We show that bivalve oxygen isotope data are recording multidecadal Arctic sea ice variability and through the climate model ensemble demonstrate that external natural drivers explain up to third of this variability. Natural external forcing causes changes in sea-ice mediated export of freshwater into areas of active deep convection, affecting the strength of the Atlantic Meridional Overturning Circulation (AMOC) and thereby northward heat transport to the Arctic. This in turn leads to sustained anomalies in sea ice extent. The models capture these positive feedbacks, giving us improved confidence in their ability to simulate future sea ice in in a rapidly evolving Arctic.Natural Environment Research Council (NERC)Natural Environment Research Council (NERC)Natural Environment Research Council (NERC)Leverhulme TrustAustralian Research CouncilEuropean Union’s Horizon 202

Nonlinear landscape and cultural response to sea-level rise

Dataset S1 (separate file). Relative sea-level database for Scilly comprising directly dated radiocarbon and optically stimulated luminescence samples with corresponding metainformation (lithostratigraphy, elevation, depositional environment and indicative meaning interpretations, paleotidal range change and sea-level calculations) following the ‘HOLSEA’ (‘Geographic Variability of Holocene Relative Sea Level’) protocol (Khan et al., 2019*). Dataset S2 (separate file). Table containing pollen results as relative abundance (genus level), modelled ages and age uncertainty for pollen samples, landcover index results (community cluster numbers and nMDS ordination axes 1 and 2), foraminifera results as species counts and transfer function results as paleomarsh elevations with uncertainty (1σ). Foraminifera samples with low test concentrations have indicative ranges (from mean high water neap tides to highest astronomical tides) in place of paleomarsh elevation estimations. Foraminifera abbreviations: H.wil – Haplophragmoides wilbertii ; J.mac – Jadammina macrescens ; M.fus – Miliammina fusca ; P.ipo – Polysaccammina ipohalina ; T.inf – Trochammina infalta ; T.och – Trochammina ochracea ; A.bat - Ammonia batavus ; A.mam – Asterigerinata mamilla ; B.var – Bolivina variablis; E.cri – Elphidium crispum ; E.wil – Elphidium Williamsoni ; F.spp. – Fissurina spp. ; Elphidium spp. ; H.ger – Haynesina germanica ; L.lob – Lobatula lobatula ; O.spp. – Oolha spp. ; Q.sem – Quinqueloculina seminula; R.spp. – Rosalina spp.. Dataset S3 (separate file). Database containing three worksheets for developing archaeological indices for Scilly. ‘SWBritain’ – Radiocarbon dates from Devon and Cornwall used to develop a summed probability distribution curve as an estimate of population demographic variation in Southwest Britain. ‘NWFrance’ - Radiocarbon dates from Brittany and Normandy used to develop a summed probability distribution curve as an estimate of population demography in Northwest France. ‘Scilly’ – Archaeological monuments from Scilly used to develop a probabilistic index of population variability.The article associated with these datasets is located in ORE at: http://hdl.handle.net/10871/123489Rising sea levels have been associated with human migration and behavioral shifts throughout prehistory, often with an emphasis on landscape submergence and consequent societal collapse. However, the assumption that future sea-level rise will drive similar adaptive responses is overly simplistic. Whilst the change from land to sea represents a dramatic and permanent shift for pre-existing human populations, the process of change is driven by a complex set of physical and cultural processes with long transitional phases of landscape and socio-economic change. Here we use reconstructions of prehistoric sea-level rise, paleogeographies, terrestrial landscape change and human population dynamics to show how the gradual inundation of an island archipelago resulted in decidedly non-linear landscape and cultural responses to rising sea-levels. Interpretation of past and future responses to sea-level change requires a better understanding of local physical and societal contexts to assess plausible human response patterns in the future.Historic EnglandWelsh GovernmentHigher Education Funding Council for Wale

Denudation of the continental shelf between Britain and France at the glacial-interglacial timescale

The erosional morphology preserved at the sea bed in the eastern English Channel dominantly records denudation of the continental shelf by fluvial processes over multiple glacial-interglacial sea-level cycles rather than by catastrophic flooding through the Straits of Dover during the mid-Quaternary. Here, through the integration of multibeam bathymetry and shallow sub-bottom 2D seismic reflection profiles calibrated with vibrocore records, the first stratigraphic model of erosion and deposition on the eastern English Channel continental shelf is presented. Published Optical Stimulated Luminescence (OSL) and C ages were used to chronometrically constrain the stratigraphy and allow correlation of the continental shelf record with major climatic/sea-level periods. Five major erosion surfaces overlain by discrete sediment packages have been identified. The continental shelf in the eastern English Channel preserves a record of processes operating from Marine Isotope Stage (MIS) 6 to MIS 1. Planar and channelised erosion surfaces were formed by fluvial incision during lowstands or relative sea-level fall. The depth and lateral extent of incision was partly conditioned by underlying geology (rock type and tectonic structure), climatic conditions and changes in water and sediment discharge coupled to ice sheet dynamics and the drainage configuration of major rivers in Northwest Europe. Evidence for major erosion during or prior to MIS 6 is preserved. Fluvial sediments of MIS 2 age were identified within the Northern Palaeovalley, providing insights into the scale of erosion by normal fluvial regimes. Seismic and sedimentary facies indicate that deposition predominantly occurred during transgression when accommodation was created in palaeovalleys to allow discrete sediment bodies to form. Sediment reworking over multiple sea-level cycles (Saalian-Eemian-early Weichselian) by fluvial, coastal and marine processes created a multi-lateral, multi-storey succession of palaeovalley-fills that are preserved as a strath terrace. The data presented here reveal a composite erosional and depositional record that has undergone a high degree of reworking over multiple sea-level cycles leading to the preferential preservation of sediments associated with the most recent glacial-interglacial period

Fundamental questions and applications of sclerochronology: Community-defined research priorities.

Horizon scanning is an increasingly common strategy to identify key research needs and frame future agendas in science. Here, we present the results of the first such exercise for the field of sclerochronology, thereby providing an overview of persistent and emergent research questions that should be addressed by future studies. Through online correspondence following the 5th International Sclerochronology Conference in 2019, participants submitted and rated questions that addressed either knowledge gaps or promising applications of sclerochronology. An initial list of 130 questions was compiled based on contributions of conference attendees and reviewed by expert panels formed during the conference. Herein, we present and discuss the 50 questions rated to be of the highest priority, determined through an online survey distributed to sclerochronology community members post the conference. The final list (1) includes important questions related to mechanisms of biological control over biomineralization, (2) highlights state of the art applications of sclerochronological methods and data for solving long-standing questions in other fields such as climate science and ecology, and (3) emphasizesthe need for common standards for data management and analysis. Although research priorities are continually reassessed, our list provides a roadmap that can be used to motivate research efforts and advance sclerochronology towardnew, and more powerful, applications.N/

Fundamental questions and applications of sclerochronology: Community-defined research priorities

Horizon scanning is an increasingly common strategy to identify key research needs and frame future agendas in science. Here, we present the results of the first such exercise for the field of sclerochronology, thereby providing an overview of persistent and emergent research questions that should be addressed by future studies. Through online correspondence following the 5th International Sclerochronology Conference in 2019, participants submitted and rated questions that addressed either knowledge gaps or promising applications of sclerochronology. An initial list of 130 questions was compiled based on contributions of conference attendees and reviewed by expert panels formed during the conference. Herein, we present and discuss the 50 questions rated to be of the highest priority, determined through an online survey distributed to sclerochronology community members post the conference. The final list: (1) includes important questions related to mechanisms of biological control over biomineralization; (2) highlights state of the art applications of sclerochronological methods and data for solving long-standing questions in other fields such as climate science and ecology: and (3) emphasizes the need for common standards for data management and analysis. Although research priorities are continually reassessed, our list provides a roadmap that can be used to motivate research efforts and advance sclerochronology toward new, and more powerful, applications

Bivariate normal mixture spread option valuation

We discuss the pricing and hedging of European spread options on correlated assets when the marginal distribution of each asset return is assumed to be a mixture of normal distributions. Being a straightforward two-dimensional generalization of a normal mixture diffusion model, the prices and hedge ratios have a firm behavioural and theoretical foundation. In this 'bivariate normal mixture' (BNM) model no-arbitrage option values are just weighted sums of different '2GBM' option values that are based on the assumption of two correlated lognormal diffusions, and likewise for their sensitivities. The main advantage of this approach is that BNM option values are consistent with both volatility smiles and with the implied correlation 'frown'. No other 'frown consistent' spread option valuation model has such straightforward implementation. We apply analytic approximations to compare BNM valuations of European spread options with those based on the 2GBM assumption and explain the differences between the two as a weighted sum of six second-order 2GBM sensitivities. We also examine BNM option sensitivities, finding that these, like the option values, can sometimes differ substantially from those obtained under the 2GBM model. Finally, we show how the correlation frown that is implied by the BNM model is affected as we change (a) the correlation structure and (b) the tail probabilities in the joint density of the asset returns.