Reconciling Open Interest with Traded Volume in Perpetual Swaps

Perpetual swaps are derivative contracts that allow traders to speculate on, or hedge, the price movements of cryptocurrencies. Unlike futures contracts perpetual swaps have no settlement or expiration, in the traditional sense. The funding rate acts as the mechanism that tethers the perpetual swap to its underlying with the help of arbitrageurs. Open interest, in the context of perpetual swaps and derivative contracts in general, refers to the total number of outstanding contracts at a given point in time. It is a critical metric in derivatives markets as it can provide insight into market activity, sentiment and overall liquidity. It also provides a way to estimate a lower bound on the collateral required for every cryptocurrency market on an exchange. This number, cumulated across all markets on the exchange in combination with proof of reserves can be used to gauge whether the exchange in question operates with unsustainable levels of leverage; which could have solvency implications. We find that open interest in bitcoin perpetual swaps is systematically misquoted by some of the largest derivatives exchanges. However, the degree varies; with some exchanges reporting open interest that is wholly implausible to others that seem to be delaying messages of forced trades, i.e. liquidations. We identify these incongruities by analyzing tick-by-tick data for two time periods in 2023 by connecting directly to seven of the most liquid cryptocurrency derivatives exchanges.Comment: 10 pages, 2 figures, 5 table

Axisymmetric MHD Modes in Twisted Magnetic Fields

Vortex flows in the solar atmosphere may contribute significantly to the energy flux requirements for heating the quiet Sun atmosphere. This thesis presents evidence that the expected number of vortices in the solar photosphere is significantly larger than estimated and most importantly their lifetime is, in the mean, much shorter than previously believed. This suggests that vortex flows are highly dynamic and that their formation and dissolution is highly temporally localised. The measurements and statistics that support this evidence were made possible by use of an automated vortex identification approach which allowed for a much larger sample. In fact the number of identified vortices is several orders of magnitude larger compared with the latest research on the subject. Given that vortices in the solar photosphere can introduce magnetic twist, a pertinent question then is: "How would that magnetic twist affect axisymmetric MHD modes?". Part of this thesis visits this question and the theoretical models used offer interesting answers. Firstly, even for weak magnetic twist the long wavelength cut-off for the sausage mode that is present in models without magnetic twist, is removed! It is shown that magnetic twist naturally couples axisymmetric Alfven waves with sausage waves. A coupling that results, among other things, in sausage waves exhibiting Doppler signatures similar to these expected to be observed in Alfven waves. These modes can also be excited by a larger variety of drivers compared to the pure sausage and axisymmetric Alfven waves. Something that makes them more pertinent to the question of energy propagation than their pure cousins (sausage and Alfven waves). Lastly, a calculation is presented, for the first time, of a dispersion relation for resonantly damped axisymmetric modes, in the spectrum of the Alfven continuum and also an approximation is presented of the damping time in the long wavelength limit. It is shown that the damping times can be comparable to that observed for the kink mode in the case that there is no magnetic twist

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

Nonconvex Many-Objective Optimisation

As many-objective optimisation problems become more prevalent, evolutionary algorithms that are based on Pareto dominance relations are slowly becoming less popular due to severe limitations that such an approach has for this class of problems. At the same time decomposition-based methods, which have been employed traditionally in mathematical programming, are consistently increasing in popularity. These developments have been led by recent research studies that show that decomposition-based algorithms have very good convergence properties compared to Pareto-based algorithms. Decomposition-based methods use a scalarising function to decompose a problem with multiple objectives into several single objective subproblems. The subproblems are defined with the help of weighting vectors. The location on the Pareto front that each subproblem tends to converge, strongly depends on the choice of weighting vectors and the scalarising function. Therefore, the selection of an appropriate set of weighting vectors to decompose the multi-objective problem, determines the distribution of the final Pareto set approximation along the Pareto front. Currently a limiting factor in decomposition-based methods is that the distribution of Pareto optimal points cannot be directly controlled, at least not to a satisfactory degree. Generalised Decomposition is introduced in this thesis as a way to optimally solve this problem and enable the analyst and the decision maker define and obtain the desired distribution of Pareto optimal solutions. Furthermore, many algorithms generate a set of Pareto optimal solutions. An interesting question is whether such a set can be used to generate more solutions in specific locations of the Pareto front. Pareto Estimation - a method introduced in this thesis - answers this question quite positively. The decision maker, using the Pareto Estimation method can request a set of solutions in a particular region on the Pareto front, and although not guaranteed to be generated in the exact location, it is shown that the spatial accuracy of the produced solutions is very high. Also the cost of generating these solutions is several orders of magnitude lower compared with the alternative to restart the optimisation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Liger - An Open Source Integrated Optimization Environment

Although there exists a number of optimization frameworks only commercial and closed source software address, to an extent, real-world optimization problems and arguably these software packages are not very easy to use. In this work we introduce an open source integrated optimization environment which is designed to be extensible and have a smooth learning curve so that it can be used by the non-expert in industry. We call this environment, Liger. Liger is an application that is built about a visual programming language, by which optimization work-flows can be created. Additionally, Liger provides a communication layer with external tools, whose functionality can be directly integrated and used with native components. This fosters code reuse and further reduces the required effort on behalf of the practitioner in order to obtain a solution to the optimization problem. Furthermore, there exists a number of available algorithms which are fully configurable, however should the need arise new algorithms can also be created just as easily by reusing what we call operator nodes. Operator nodes perform specific tasks on a set, or a single solution. Lastly as visual exploration of the obtained solutions is essential for decision makers, we also provide state-of-the art visualization capabilities