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Register a new userMalliavin-Mancino estimators implemented with non-uniform fast Fourier transforms
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We implement and test kernel averaging Non-Uniform Fast Fourier Transform (NUFFT) methods to enhance the performance of correlation and covariance estimation on asynchronously sampled event-data using the Malliavin-Mancino Fourier estimator. The methods are benchmarked for Dirichlet and Fej{e}r Fourier basis kernels. We consider test cases formed from Geometric Brownian motions to replicate synchronous and asynchronous data for benchmarking purposes. We consider three standard averaging kernels to convolve the event-data for synchronisation via over-sampling for use with the Fast Fourier Transform (FFT): the Gaussian kernel, the Kaiser-Bessel kernel, and the exponential of semi-circle kernel. First, this allows us to demonstrate the performance of the estimator with different combinations of basis kernels and averaging kernels. Second, we investigate and compare the impact of the averaging scales explicit in each averaging kernel and its relationship between the time-scale averaging implicit in the Malliavin-Mancino estimator. Third, we demonstrate the relationship between time-scale averaging based on the number of Fourier coefficients used in the estimator to a theoretical model of the Epps effect. We briefly demonstrate the methods on Trade-and-Quote (TAQ) data from the Johannesburg Stock Exchange to make an initial visualisation of the correlation dynamics for various time-scales under market microstructure.
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We compare the Malliavin-Mancino and Cuchiero-Teichmann Fourier instantaneous estimators to investigate the impact of the Epps effect arising from asynchrony in the instantaneous estimates. We demonstrate the instantaneous Epps effect under a simulation setting and provide a simple method to ameliorate the effect. We find that using the previous tick interpolation in the Cuchiero-Teichmann estimator results in unstable estimates when dealing with asynchrony, while the ability to bypass the time domain with the Malliavin-Mancino estimator allows it to produce stable estimates and is therefore better suited for ultra-high frequency finance. An empirical analysis using Trade and Quote data from the Johannesburg Stock Exchange illustrates the instantaneous Epps effect and how the intraday correlation dynamics can vary between days for the same equity pair.
The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results.
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of non-uniform sampled planes is limited due to the property of the FFT that imposes uniform sampling. In addition, it gives rise to wasteful sampling data if we calculate a plane having locally low and high spatial frequencies. In this paper, we developed non-uniform sampled ASM and Fresnel diffraction to improve the problem using the non-uniform FFT.
The dynamics of financial markets are driven by the interactions between participants, as well as the trading mechanisms and regulatory frameworks that govern these interactions. Decision-makers would rather not ignore the impact of other participants on these dynamics and should employ tools and models that take this into account. To this end, we demonstrate the efficacy of applying opponent-modeling in a number of simulated market settings. While our simulations are simplified representations of actual market dynamics, they provide an idealized playground in which our techniques can be demonstrated and tested. We present this work with the aim that our techniques could be refined and, with some effort, scaled up to the full complexity of real-world market scenarios. We hope that the results presented encourage practitioners to adopt opponent-modeling methods and apply them online systems, in order to enable not only reactive but also proactive decisions to be made.
Flash Loan attack can grab millions of dollars from decentralized vaults in one single transaction, drawing increasing attention from the Decentralized Finance (DeFi) players. It has also demonstrated an exciting opportunity that a huge wealth could be created by composing DeFis building blocks and exploring the arbitrage change. However, a fundamental framework to study the field of DeFi has not yet reached a consensus and theres a lack of standard tools or languages to help better describe, design and improve the running processes of the infant DeFi systems, which naturally makes it harder to understand the basic principles behind the complexity of Flash Loan attacks. In this paper, we are the first to propose Flashot, a prototype that is able to transparently illustrate the precise asset flows intertwined with smart contracts in a standardized diagram for each Flash Loan event. Some use cases are shown and specifically, based on Flashot, we study a typical Pump and Arbitrage case and present in-depth economic explanations to the attackers behaviors. Finally, we conclude the development trends of Flash Loan attacks and discuss the great impact on DeFi ecosystem brought by Flash Loan. We envision a brand new quantitative financial industry powered by highly efficient automatic risk and profit detection systems based on the blockchain.
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