Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust

A well-known result by Vega-Redondo implies that in symmetric Cournot oligopoly, imitation leads to the Walrasian outcome where price equals marginal cost. In this paper we show that this result is not robust to the slightest asymmetry in fixed costs. Instead of obtaining the Walrasian outcome as unique prediction, every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is still a good predictor of behavior.

A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics

A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.Smile, local volatility, generalized additive model, backfitting, functional principal component analysis

Field Trials for the Empirical Characterization of the Low Voltage Grid Access Impedance From 35 kHz to 500 kHz

The access impedance of low-voltage (LV) power networks is a major factor related to the performance of the narrow-band power line communications (NB-PLCs) and, in a wider sense, to electromagnetic compatibility (EMC) performance. Up to date, there is still a lack of knowledge about the frequency-dependent access impedance for frequencies above 9 kHz and up to 500 kHz, which is the band where the NB-PLC operates. The access impedance affects the transmission of the NB-PLC signal, and it determines the propagation of the non-intentional emissions that may disturb other electrical devices, including malfunctioning or reduced lifetime of equipment. This paper presents the results of field measurements of the LV access impedance up to 500 kHz in different scenarios, with measurement locations close to end users and near transformers. The results provide useful information to analyze the characteristics of the LV access impedance, including variation with frequency, ranges of values for different frequency bands, and analysis of specific phenomena. Moreover, the results reveal a diverse frequency-dependent behavior of the access impedance in different scenarios, depending on the grid topology, the number of end users (that is, number and type of connected loads), and the type of transformation center. Overall, the results of this paper offer a better understanding of the transmission of NB-PLC signals and EMC-related phenomena.The authors would like to thank Iberdrola for the availability and the collaboration of authorized staff for carrying out the field trials

Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust

A well-known result by Vega-Redondo (1997) implies that in symmetric Cournot oligopoly, imitation leads to the Walrasian outcome where price equals marginal cost. In this paper, we show that this result is not robust to the slightest asymmetry in fixed costs. Instead of obtaining the Walrasian outcome as unique prediction, every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is still a good predictor of behavior.evolutionary game theory, stochastic stability, imitation, Cournot markets, information, experiments, simulations

Multi-conjugated adaptive optics imaging of distant galaxies -- A comparison of Gemini/GSAOI and VLT/HAWK-I data

Multi-conjugated adaptive optics (MCAO) yield nearly diffraction-limited images at 2$\mu$m wavelengths. Currently, GeMS/GSAOI at Gemini South is the only MCAO facility instrument at an 8m telescope. Using real data and for the first time, we investigate the gain in depth and S/N when MCAO is employed for $K_{\rm s}$-band observations of distant galaxies. Our analysis is based on the Frontier Fields cluster MACS J0416.1-2403, observed with GeMS/GSAOI (near diffraction-limited) and compared against VLT/HAWK-I (natural seeing) data. Using galaxy number counts, we show that the substantially increased thermal background and lower optical throughput of the MCAO unit are fully compensated for by the wavefront correction, because the galaxy images can be measured in smaller apertures with less sky noise. We also performed a direct comparison of the signal-to-noise ratios (S/N) of sources detected in both data sets. For objects with intrinsic angular sizes corresponding to half the HAWK-I image seeing, the gain in S/N is 40 per cent. Even smaller objects experience a boost in S/N by a up to a factor of 2.5 despite our suboptimal natural guide star configuration. The depth of the near diffraction limited images is more difficult to quantify than that of seeing limited images, due to a strong dependence on the intrinsic source profiles. Our results emphasize the importance of cooled MCAO systems for $K_{\rm s}$-band observations with future, extremely large telescopes.Comment: 7 pages, 7 figures. Accepted for publication in MNRA

Pricing options and computing implied volatilities using neural networks

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly