Proximity of Bachelier and Samuelson Models for Different Metrics

This paper proposes a method of comparing the prices of European options, based on the use of probabilistic metrics, with respect to two models of price dynamics: Bachelier and Samuelson. In contrast to other studies on the subject, we consider two classes of options: European options with a Lipschitz continuous payout function and European options with a bounded payout function. For these classes, the following suitable probability metrics are chosen: the Fortet-Maurier metric, the total variation metric, and the Kolmogorov metric. It is proved that their computation can be reduced to computation of the Lambert in case of the Fortet-Mourier metric, and to the solution of a nonlinear equation in other cases. A statistical estimation of the model parameters in the modern oil market gives the order of magnitude of the error, including the magnitude of sensitivity of the option price, to the change in the volatility.

ENSO Prediction in Project Minerva: Sensitivity to Atmospheric Horizontal Resolution and Ensemble Size

This study examines El Niño–Southern Oscillation (ENSO) prediction in Project Minerva, a recent collaboration between the Center for Ocean–Land–Atmosphere Studies (COLA) and the European Centre for Medium-Range Weather Forecasts (ECMWF). The focus is primarily on the impact of the atmospheric horizontal resolution on ENSO prediction, but the effect from different ensemble sizes is also discussed. Particularly, three sets of 7-month hindcasts performed with ECMWF prediction system are compared, starting from 1 May (1 November) during 1982–2011 (1982–2010): spectral T319 atmospheric resolution with 15 ensembles, spectral T639 with 15 ensembles, and spectral T319 with 51 ensembles. The analysis herein shows that simply increasing either ensemble size from 15 to 51 or atmospheric horizontal resolution from T319 to T639 does not necessarily lead to major improvement in the ENSO prediction skill with current climate models. For deterministic prediction skill metrics, the three sets of predictions do not produce a significant difference in either anomaly correlation or root-mean-square error (RMSE). For probabilistic metrics, the increased atmospheric horizontal resolution generates larger ensemble spread, and thus increases the ratio between the intraensemble spread and RMSE. However, there is little change in the categorical distributions of predicted SST anomalies, and consequently there is little difference among the three sets of hindcasts in terms of probabilistic metrics or prediction reliability.

Query Based Topic Modeling

Finally, in order to compare the QTM results with models generated by other methods we have developed probabilistic metrics that formalize the notion of semantic coherence using probabilistic concepts and can be used to validate overlapping and incomplete clustering using multi-labeled corpora. They show that the proposed method can produce models of comparable, or even superior quality, than those produced with state of the art probabilistic methods.