Calibration of optimal execution of financial transactions in the presence of transient market impact

Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate with real data the optimal execution problem both for risk neutral and for risk averse investors and we derive an efficient frontier of optimal execution. When we include spread costs the problem must be solved numerically and we show that the introduction of such costs regularizes the solution.Comment: 31 pages, 8 figure

SciPy 1.0: fundamental algorithms for scientific computing in Python.

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments

A second generation human haplotype map of over 3.1 million SNPs

We describe the Phase II HapMap, which characterizes over 3.1 million human single nucleotide polymorphisms (SNPs) genotyped in 270 individuals from four geographically diverse populations and includes 25-35% of common SNP variation in the populations surveyed. The map is estimated to capture untyped common variation with an average maximum r(2) of between 0.9 and 0.96 depending on population. We demonstrate that the current generation of commercial genome-wide genotyping products captures common Phase II SNPs with an average maximum r(2) of up to 0.8 in African and up to 0.95 in non-African populations, and that potential gains in power in association studies can be obtained through imputation. These data also reveal novel aspects of the structure of linkage disequilibrium. We show that 10-30% of pairs of individuals within a population share at least one region of extended genetic identity arising from recent ancestry and that up to 1% of all common variants are untaggable, primarily because they lie within recombination hotspots. We show that recombination rates vary systematically around genes and between genes of different function. Finally, we demonstrate increased differentiation at non-synonymous, compared to synonymous, SNPs, resulting from systematic differences in the strength or efficacy of natural selection between populations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62863/1/nature06258.pd

Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python (Nature Methods, (2020), 17, 3, (261-272), 10.1038/s41592-019-0686-2)

An amendment to this paper has been published and can be accessed via a link at the top of the paper

A haplotype map of the human genome

Inherited genetic variation has a critical but as yet largely uncharacterized role in human disease. Here we report a public database of common variation in the human genome: more than one million single nucleotide polymorphisms (SNPs) for which accurate and complete genotypes have been obtained in 269 DNA samples from four populations, including ten 500-kilobase regions in which essentially all information about common DNA variation has been extracted. These data document the generality of recombination hotspots, a block-like structure of linkage disequilibrium and low haplotype diversity, leading to substantial correlations of SNPs with many of their neighbours. We show how the HapMap resource can guide the design and analysis of genetic association studies, shed light on structural variation and recombination, and identify loci that may have been subject to natural selection during human evolution

Genome-wide detection and characterization of positive selection in human populations

With the advent of dense maps of human genetic variation, it is now possible to detect positive natural selection across the human genome. Here we report an analysis of over 3 million polymorphisms from the International HapMap Project Phase 2 (HapMap2). We used 'long-range haplotype' methods, which were developed to identify alleles segregating in a population that have undergone recent selection, and we also developed new methods that are based on cross-population comparisons to discover alleles that have swept to near-fixation within a population. The analysis reveals more than 300 strong candidate regions. Focusing on the strongest 22 regions, we develop a heuristic for scrutinizing these regions to identify candidate targets of selection. In a complementary analysis, we identify 26 non-synonymous, coding, single nucleotide polymorphisms showing regional evidence of positive selection. Examination of these candidates highlights three cases in which two genes in a common biological process have apparently undergone positive selection in the same population:LARGE and DMD, both related to infection by the Lassa virus, in West Africa;SLC24A5 and SLC45A2, both involved in skin pigmentation, in Europe; and EDAR and EDA2R, both involved in development of hair follicles, in Asia