Monte Carlo methods for the valuation of multiple exercise options

We discuss Monte Carlo methods for valuing options with multiple exercise features in discrete time. By extending the recently developed duality ideas for American option pricing we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets

Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 - Part 1: Model description and calibration

Current scientific knowledge on the future response of the climate system to human-induced perturbations is comprehensively captured by various model intercomparison efforts. In the preparation of the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), intercomparisons were organized for atmosphere-ocean general circulation models (AOGCMs) and carbon cycle models, named "CMIP3" and "C4MIP", respectively. Despite their tremendous value for the scientific community and policy makers alike, there are some difficulties in interpreting the results. For example, radiative forcings were not standardized across the various AOGCM integrations and carbon cycle runs, and, in some models, key forcings were omitted. Furthermore, the AOGCM analysis of plausible emissions pathways was restricted to only three SRES scenarios. This study attempts to address these issues. We present an updated version of MAGICC, the simple carbon cycle-climate model used in past IPCC Assessment Reports with enhanced representation of time-varying climate sensitivities, carbon cycle feedbacks, aerosol forcings and ocean heat uptake characteristics. This new version, MAGICC6, is successfully calibrated against the higher complexity AOGCMs and carbon cycle models. Parameterizations of MAGICC6 are provided. The mean of the emulations presented here using MAGICC6 deviates from the mean AOGCM responses by only 2.2% on average for the SRES scenarios. This enhanced emulation skill in comparison to previous calibrations is primarily due to: making a "like-with-like comparison" using AOGCM-specific subsets of forcings; employing a new calibration procedure; as well as the fact that the updated simple climate model can now successfully emulate some of the climate-state dependent effective climate sensitivities of AOGCMs. The diagnosed effective climate sensitivity at the time of CO2 doubling for the AOGCMs is on average 2.88 °C, about 0.33 °C cooler than the mean of the reported slab ocean climate sensitivities. In the companion paper (Part 2) of this study, we examine the combined climate system and carbon cycle emulations for the complete range of IPCC SRES emissions scenarios and the new RCP pathways

Climate change under a scenario near 1.5° C of global warming: Monsoon intensification, ocean warming and steric sea level rise

We present climatic consequences of the Representative Concentration Pathways (RCPs) using the coupled climate model CLIMBER-3α, which contains a statistical-dynamical atmosphere and a three-dimensional ocean model. We compare those with emulations of 19 state-of-the-art atmosphere-ocean general circulation models (AOGCM) using MAGICC6. The RCPs are designed as standard scenarios for the forthcoming IPCC Fifth Assessment Report to span the full range of future greenhouse gas (GHG) concentrations pathways currently discussed. The lowest of the RCP scenarios, RCP3-PD, is projected in CLIMBER-3α to imply a maximal warming by the middle of the 21st century slightly above 1.5 °C and a slow decline of temperatures thereafter, approaching today's level by 2500. We identify two mechanisms that slow down global cooling after GHG concentrations peak: The known inertia induced by mixing-related oceanic heat uptake; and a change in oceanic convection that enhances ocean heat loss in high latitudes, reducing the surface cooling rate by almost 50%. Steric sea level rise under the RCP3-PD scenario continues for 200 years after the peak in surface air temperatures, stabilizing around 2250 at 30 cm. This contrasts with around 1.3 m of steric sea level rise by 2250, and 2 m by 2500, under the highest scenario, RCP8.5. Maximum oceanic warming at intermediate depth (300–800 m) is found to exceed that of the sea surface by the second half of the 21st century under RCP3-PD. This intermediate-depth warming persists for centuries even after surface temperatures have returned to present-day values, with potential consequences for marine ecosystems, oceanic methane hydrates, and ice-shelf stability. Due to an enhanced land-ocean temperature contrast, all scenarios yield an intensification of monsoon rainfall under global warming

Analysis of the Copenhagen Accord pledges and its global climatic impacts‚ a snapshot of dissonant ambitions

This analysis of the Copenhagen Accord evaluates emission reduction pledges by individual countries against the Accord's climate-related objectives. Probabilistic estimates of the climatic consequences for a set of resulting multi-gas scenarios over the 21st century are calculated with a reduced complexity climate model, yielding global temperature increase and atmospheric CO2 and CO2-equivalent concentrations. Provisions for banked surplus emission allowances and credits from land use, land-use change and forestry are assessed and are shown to have the potential to lead to significant deterioration of the ambition levels implied by the pledges in 2020. This analysis demonstrates that the Copenhagen Accord and the pledges made under it represent a set of dissonant ambitions. The ambition level of the current pledges for 2020 and the lack of commonly agreed goals for 2050 place in peril the Accord's own ambition: to limit global warming to below 2 °C, and even more so for 1.5 °C, which is referenced in the Accord in association with potentially strengthening the long-term temperature goal in 2015. Due to the limited level of ambition by 2020, the ability to limit emissions afterwards to pathways consistent with either the 2 or 1.5 °C goal is likely to become less feasibl

Emulating IPCC AR4 atmosphere-ocean and carbon cycle models for projecting global-mean, hemispheric and land/ocean temperatures: MAGICC 6.0

International audienceCurrent scientific knowledge on the future response of the climate system to human-induced perturbations is comprehensively captured by various model intercomparison efforts. In the preparation of the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), intercomparisons were organized for atmosphere-ocean general circulation models (AOGCMs) and carbon cycle models, named "CMIP3" and "C4MIP", respectively. Despite their tremendous value for the scientific community and policy makers alike, there are some difficulties in interpreting the results. For example, key radiative forcings have not been considered or standardized in the majority of AOGCMs integrations and carbon cycle runs. Furthermore, the AOGCM analysis of plausible emission pathways was restricted to only three SRES scenarios. This study attempts to address these issues. We present an updated version of MAGICC, the simple carbon cycle-climate model used in past IPCC Assessment Reports with enhanced representation of time-varying climate sensitivities, carbon cycle feedbacks, aerosol forcings and ocean heat uptake characteristics. This new version of MAGICC (6.0) is successfully calibrated against the higher complexity AOGCM and carbon cycle models. Parameterizations of MAGICC 6.0 are provided. Previous MAGICC versions and emulations shown in IPCC AR4 (WG1, Fig. 10.26, page 803) yielded, in average, a 10% larger global-mean temperature increase over the 21st century compared to the AOGCMs. The reasons for this difference are discussed. The emulations presented here using MAGICC 6.0 match the mean AOGCM responses to within 2.2% for the SRES scenarios. This enhanced emulation skill is due to: the comparison on a "like-with-like" basis using AOGCM-specific subsets of forcings, a new calibration procedure, as well as the fact that the updated simple climate model can now successfully emulate some of the climate-state dependent effective climate sensitivities of AOGCMs. The mean diagnosed effective climate sensitivities of the AOGCMs is 2.88°C, about 0.33°C cooler than the reported slab ocean climate sensitivities. Finally, we examine the combined climate system and carbon cycle emulations for the complete range of IPCC SRES emission scenarios and some lower mitigation pathways

Emulating Atlantic overturning strength for low emission scenarios: Consequences for sea-level rise along the North American east coast

In order to provide probabilistic projections of the future evolution of the Atlantic Meridional Overturning Circulation (AMOC), we calibrated a simple Stommeltype box model to emulate the output of fully coupled threedimensional atmosphere-ocean general circulation models (AOGCMs) of the Coupled Model Intercomparison Project (CMIP). Based on this calibration to idealised global warming scenarios with and without interactive atmosphere-ocean fluxes and freshwater perturbation simulations, we project the future evolution of the AMOC mean strength within the covered calibration range for the lower two Representative Concentration Pathways (RCPs) until 2100 obtained from the reduced complexity carbon cycle-climate model MAGICC 6. For RCP3-PD with a global mean temperature median below 1.0 C warming relative to the year 2000, we project an ensemble median weakening of up to 11% compared to 22% under RCP4.5 with a warming median up to 1.9 C over the 21st century. Additional Greenland meltwater of 10 and 20 cm of global sea-level rise equivalent further weakens the AMOC by about 4.5 and 10 %, respectively. By combining our outcome with a multi-model sea-level rise study we project a dynamic sea-level rise along the New York City coastline of 4 cm for the RCP3-PD and of 8 cm for the RCP4.5 scenario over the 21st century. We estimate the total steric and dynamic sea-level rise for New York City to be about 24 cm until 2100 for the RCP3-PD scenario, which can hold as a lower bound for sea-level rise projections in this region, as it does not include ice sheet and mountain glacier contributions

Implications of non-linearities between cumulative CO2 emissions and CO2-induced warming for assessing the remaining carbon budget

To determine the remaining carbon budget, a new framework was introduced in the Intergovernmental Panel on Climate Change's Special Report on Global Warming of 1.5 °C (SR1.5). We refer to this as a 'segmented' framework because it considers the various components of the carbon budget derivation independently from one another. Whilst implementing this segmented framework, in SR1.5 the assumption was that there is a strictly linear relationship between cumulative CO2 emissions and CO2-induced warming i.e. the TCRE is constant and can be applied to a range of emissions scenarios. Here we test whether such an approach is able to replicate results from model simulations that take the climate system's internal feedbacks and non-linearities into account. Within our modelling framework, following the SR1.5's choices leads to smaller carbon budgets than using simulations with interacting climate components. For 1.5 °C and 2 °C warming targets, the differences are 50 GtCO2 (or 10%) and 260 GtCO2 (or 17%), respectively. However, by relaxing the assumption of strict linearity, we find that this difference can be reduced to around 0 GtCO2 for 1.5 °C of warming and 80 GtCO2 (or 5%) for 2.0 °C of warming (for middle of the range estimates of the carbon cycle and warming response to anthropogenic emissions). We propose an updated implementation of the segmented framework that allows for the consideration of non-linearities between cumulative CO2 emissions and CO2-induced warming

A roadmap for rapid decarbonization

Although the Paris Agreement's goals (1) are aligned with science (2) and can, in principle, be technically and economically achieved (3), alarming inconsistencies remain between science-based targets and national commitments. Despite progress during the 2016 Marrakech climate negotiations, long-term goals can be trumped by political short-termism. Following the Agreement, which became international law earlier than expected, several countries published mid-century decarbonization strategies, with more due soon. Model-based decarbonization assessments (4) and scenarios often struggle to capture transformative change and the dynamics associated with it: disruption, innovation, and nonlinear change in human behavior. For example, in just 2 years, China's coal use swung from 3.7% growth in 2013 to a decline of 3.7% in 2015 (5). To harness these dynamics and to calibrate for short-term realpolitik, we propose framing the decarbonization challenge in terms of a global decadal roadmap based on a simple heuristic—a “carbon law”—of halving gross anthropogenic carbon-dioxide (CO2) emissions every decade. Complemented by immediately instigated, scalable carbon removal and efforts to ramp down land-use CO2 emissions, this can lead to net-zero emissions around mid-century, a path necessary to limit warming to well below 2°C