This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a time-varying correlation. Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for shortdated options.JEL classification: G12, C11. Evidence from Underlying and Options MarketsThis paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and risk-neutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a time-varying correlation.Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for short-dated options.

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Nitrate-N concentrations in the Raccoon River have increased beginning in the early 1970s. Since this river is the predominant water supply for the City of Des Moines in Iowa, there is concern about the potential long-term impacts of these trends. Improvements in water quality from agricultural watersheds are critical to protect the water supply, and understanding the factors affecting water quality will lead to potential changes in agricultural management to improve water quality. The historical database of nitrate-nitrogen (NO 3 -N) concentrations sampled at the Des Moines Water Works were combined with observations on N fertilizer use, animal production, crop yields, land-use changes, and precipitation patterns to evaluate these interrelationships. Mean annual NO 3 -N concentrations in the Raccoon River watershed have been increasing since 1970 in spite of no significant change in N fertilizer use for the past 15 years. There have been three years with maximum NO 3 -N concentrations above 18 mg L -1 . However, these spikes occurred throughout the past 30 years and are not isolated to the last 10 years of record. Nitrate-N loads from the Raccoon River watershed have shown a slight decrease in the past ten years because of the increased crop yields and increased removal of N in the corn (Zea mays L.) and soybean (Gylcine max [L.] Merr.) grains. Production numbers for cattle have decreased by 63% since the early 1980s, while hogs have shown a 20% decrease over the same time period. Therefore, N available for application into the basin has decreased by 25%. Annual variations in NO 3 -N loads are significantly related to precipitation in the first five months of the year. A significant correlation was found between the land area within the watershed cropped to small grains and hay crops and the increase of NO 3 -N since 1970 (r = -0.76). This relationship was caused by alteration in the seasonal water-use patterns and loss of N during the fall or early spring in the water movement in contrast to corn or soybean, which have a limited N uptake pattern concentrated between June and early September. Changes in the water-use patterns caused by shifts in cropping patterns provide an explanation for the positive correlation between precipitation and flow during the early part of the year. Development of agricultural management practices that can potentially affect water quality will have to be more inclusive of all components in agricultural systems, rather than only changing fertilizer rate or timing.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.

We thank K. Baks, N. Jegadeesh, and seminar participants at Emory University for helpful comments and the BSI Gamma Foundation for financial support. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research.