The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.

A 30-yr climatology of the snow-to-liquid-equivalent ratio (SLR) using the National Weather Service (NWS) Cooperative Summary of the Day (COOP) data is presented. Descriptive statistics are presented for 96 NWS county warning areas (CWAs), along with a discussion of selected histograms of interest. The results of the climatology indicate that a mean SLR value of 13 appears more appropriate for much of the country rather than the often-assumed value of 10, although considerable spatial variation in the mean exists. The distribution for the entire dataset exhibits positive skewness. Histograms for individual CWAs are both positively and negatively skewed, depending upon the variability of the in-cloud, subcloud, and ground conditions.

Central New York State, located at the intersection of the northeastern United States and the Great Lakes basin, is impacted by snowfall produced by lake-effect and non-lake-effect snowstorms. The purpose of this study is to determine the spatiotemporal patterns of snowfall in central New York and their possible underlying causes. Ninety-three Cooperative Observer Program stations are used in this study. Spatiotemporal patterns are analyzed using simple linear regressions, Pearson correlations, principal component analysis to identify regional clustering, and spatial snowfall distribution maps in the ArcGIS software. There are three key findings. First, when the longterm snowfall trend (1931/32-2011/12) is divided into two halves, a strong increase is present during the first half (1931/32-1971/72), followed by a lesser decrease in the second half (1971/72-2011/12). This result suggests that snowfall trends behave nonlinearly over the period of record. Second, central New York spatial snowfall patterns are similar to those for the whole Great Lakes basin. For example, for five distinct regions identified within central New York, regions closer to and leeward of Lake Ontario experience higher snowfall trends than regions farther away and not leeward of the lake. Third, as compared with precipitation totals (0.02), average air temperatures had the largest significant (r , 0.05) correlation (20.56) with seasonal snowfall totals in central New York. Findings from this study are valuable because they provide a basis for understanding snowfall patterns in a region that is affected by both non-lake-effect and lake-effect snowstorms.

Abstract. Regional atmospheric CO 2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO 2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO 2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-GoldfarbShanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO 2 . The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO 2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO 2 inversions.

Anthropogenic CO 2 emission from fossil fuel combustion has major impacts on the global climate. The Orbiting Carbon Observatory 2 (OCO-2) observations have previously been used to estimate individual power plant emissions with a Gaussian plume model assuming constant wind fields. The present work assesses the feasibility of estimating power plant CO 2 emission using high resolution chemistry transport model simulations with OCO-2 observation data. In the new framework, 1.33 km Weather Research and Forecasting-Chem (WRF)-Chem simulation results are used to calculate the Jacobian matrix, which is then used with the OCO-2 XCO 2 data to obtain power plant daily mean emission rates, through a maximum likelihood estimation. We applied the framework to the seven OCO-2 observations of near mid-to-large coal burning power plants identified in Nassar et al (2017 Geophys. Res. Lett. 44, 10045-53). Our estimation results closely match the reported emission rates at the Westar power plant (Kansas, USA), with a reported value of 26.67 ktCO 2 /day, and our estimated value at 25.82-26.47 ktCO 2 /day using OCO-2 v8 data, and 22.09-22.80 ktCO 2 /day using v9 data. At Ghent, KY, USA, our estimations using three versions (v7, v8, and v9) range from 9.84-20.40 ktCO 2 /day, which are substantially lower than the reported value (29.17 ktCO 2 /day). We attribute this difference to diminished WRF-Chem wind field simulation accuracy. The results from the seven cases indicate that accurate estimation requires accurate meteorological simulations and high quality XCO 2 data. In addition, the strength and orientation (relative to the OCO-2 ground track) of the XCO 2 enhancement are important for accurate and reliable estimation. Compared with the Gaussian plume model based approach, the high resolution WRF-Chem simulation based approach provides a framework for addressing varying wind fields, and possible expansion to city level emission estimation.

This paper considers credit portfolio models based on Levy processes in general, and the gamma model in particular. It describes both single-name and multi-name situations using the gamma model, along with calibration fits and a comparison of various simple Levy models. There is also extensive historical data, including the May 2005 Auto crisis, which can be described in terms of the model. Parameter-based risk management using the gamma model is also discussed along with implementation details.

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