Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis ArXiv ID: 2305.13123 “View on arXiv” Authors: Unknown Abstract We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been proposed in the statistical literature. We put forward an alternative selection method based on a criterion coming from information theory and from the physics of complex systems: the bandwidth to be selected maximizes a new measure of complexity, with the aim of avoiding both overfitting and underfitting. We review existing methods of bandwidth selection and show that they lead to contradictory conclusions regarding the complexity of the probability distribution of price returns. This has also some striking consequences in the evaluation of the relevance of the efficient market hypothesis. We apply these methods to real financial data, focusing on the Bitcoin. ...

Deformation of Marchenko-Pastur distribution for the correlated time series ArXiv ID: 2305.12632 “View on arXiv” Authors: Unknown Abstract We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution (MPD) in the double scaling limit. When there is temporal correlation, the eigenvalue distribution converges to the deformed MPD which has a longer tail and higher peak than the MPD. Here we discuss the moments of distribution and convergence to the deformed MPD for the Gaussian process with a temporal correlation. We show that the second moment increases as the temporal correlation increases. When the temporal correlation is the power decay, we observe a phenomenon such as a phase transition. When $γ>1/2$ which is the power index of the temporal correlation, the second moment of the distribution is finite and the largest eigenvalue is finite. On the other hand, when $γ\leq 1/2$, the second moment is infinite and the largest eigenvalue is infinite. Using finite scaling analysis, we estimate the critical exponent of the phase transition. ...

InProC: Industry and Product/Service Code Classification ArXiv ID: 2305.13532 “View on arXiv” Authors: Unknown Abstract Determining industry and product/service codes for a company is an important real-world task and is typically very expensive as it involves manual curation of data about the companies. Building an AI agent that can predict these codes automatically can significantly help reduce costs, and eliminate human biases and errors. However, unavailability of labeled datasets as well as the need for high precision results within the financial domain makes this a challenging problem. In this work, we propose a hierarchical multi-class industry code classifier with a targeted multi-label product/service code classifier leveraging advances in unsupervised representation learning techniques. We demonstrate how a high quality industry and product/service code classification system can be built using extremely limited labeled dataset. We evaluate our approach on a dataset of more than 20,000 companies and achieved a classification accuracy of more than 92%. Additionally, we also compared our approach with a dataset of 350 manually labeled product/service codes provided by Subject Matter Experts (SMEs) and obtained an accuracy of more than 96% resulting in real-life adoption within the financial domain. ...

Stock and market index prediction using Informer network ArXiv ID: 2305.14382 “View on arXiv” Authors: Unknown Abstract Applications of deep learning in financial market prediction has attracted huge attention from investors and researchers. In particular, intra-day prediction at the minute scale, the dramatically fluctuating volume and stock prices within short time periods have posed a great challenge for the convergence of networks result. Informer is a more novel network, improved on Transformer with smaller computational complexity, longer prediction length and global time stamp features. We have designed three experiments to compare Informer with the commonly used networks LSTM, Transformer and BERT on 1-minute and 5-minute frequencies for four different stocks/ market indices. The prediction results are measured by three evaluation criteria: MAE, RMSE and MAPE. Informer has obtained best performance among all the networks on every dataset. Network without the global time stamp mechanism has significantly lower prediction effect compared to the complete Informer; it is evident that this mechanism grants the time series to the characteristics and substantially improves the prediction accuracy of the networks. Finally, transfer learning capability experiment is conducted, Informer also achieves a good performance. Informer has good robustness and improved performance in market prediction, which can be exactly adapted to real trading. ...

Trustless Price Feeds of Cryptocurrencies: Pathfinder ArXiv ID: 2305.13227 “View on arXiv” Authors: Unknown Abstract Price feeds of securities is a critical component for many financial services, allowing for collateral liquidation, margin trading, derivative pricing and more. With the advent of blockchain technology, value in reporting accurate prices without a third party has become apparent. There have been many attempts at trying to calculate prices without a third party, in which each of these attempts have resulted in being exploited by an exploiter artificially inflating the price. The industry has then shifted to a more centralized design, fetching price data from multiple centralized sources and then applying statistical methods to reach a consensus price. Even though this strategy is secure compared to reading from a single source, enough number of sources need to report to be able to apply statistical methods. As more sources participate in reporting the price, the feed gets more secure with the slowest feed becoming the bottleneck for query response time, introducing a tradeoff between security and speed. This paper provides the design and implementation details of a novel method to algorithmically compute security prices in a way that artificially inflating targeted pools has no effect on the reported price of the queried asset. We hypothesize that the proposed algorithm can report accurate prices given a set of possibly dishonest sources. ...

Machine Learning for Socially Responsible Portfolio Optimisation ArXiv ID: 2305.12364 “View on arXiv” Authors: Unknown Abstract Socially responsible investors build investment portfolios intending to incite social and environmental advancement alongside a financial return. Although Mean-Variance (MV) models successfully generate the highest possible return based on an investor’s risk tolerance, MV models do not make provisions for additional constraints relevant to socially responsible (SR) investors. In response to this problem, the MV model must consider Environmental, Social, and Governance (ESG) scores in optimisation. Based on the prominent MV model, this study implements portfolio optimisation for socially responsible investors. The amended MV model allows SR investors to enter markets with competitive SR portfolios despite facing a trade-off between their investment Sharpe Ratio and the average ESG score of the portfolio. ...

Predicting Stock Market Time-Series Data using CNN-LSTM Neural Network Model ArXiv ID: 2305.14378 “View on arXiv” Authors: Unknown Abstract Stock market is often important as it represents the ownership claims on businesses. Without sufficient stocks, a company cannot perform well in finance. Predicting a stock market performance of a company is nearly hard because every time the prices of a company stock keeps changing and not constant. So, its complex to determine the stock data. But if the previous performance of a company in stock market is known, then we can track the data and provide predictions to stockholders in order to wisely take decisions on handling the stocks to a company. To handle this, many machine learning models have been invented but they didn’t succeed due to many reasons like absence of advanced libraries, inaccuracy of model when made to train with real time data and much more. So, to track the patterns and the features of data, a CNN-LSTM Neural Network can be made. Recently, CNN is now used in Natural Language Processing (NLP) based applications, so by identifying the features from stock data and converting them into tensors, we can obtain the features and then send it to LSTM neural network to find the patterns and thereby predicting the stock market for given period of time. The accuracy of the CNN-LSTM NN model is found to be high even when allowed to train on real-time stock market data. This paper describes about the features of the custom CNN-LSTM model, experiments we made with the model (like training with stock market datasets, performance comparison with other models) and the end product we obtained at final stage. ...

Value-at-Risk-Based Portfolio Insurance: Performance Evaluation and Benchmarking Against CPPI in a Markov-Modulated Regime-Switching Market ArXiv ID: 2305.12539 “View on arXiv” Authors: Unknown Abstract Designing dynamic portfolio insurance strategies under market conditions switching between two or more regimes is a challenging task in financial economics. Recently, a promising approach employing the value-at-risk (VaR) measure to assign weights to risky and riskless assets has been proposed in [“Jiang C., Ma Y. and An Y. “The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis” , International Review of Financial Analysis 18(4) (2009): 185-197”]. In their study, the risky asset follows a geometric Brownian motion with constant drift and diffusion coefficients. In this paper, we first extend their idea to a regime-switching framework in which the expected return of the risky asset and its volatility depend on an unobservable Markovian term which describes the cyclical nature of asset returns in modern financial markets. We then analyze and compare the resulting VaR-based portfolio insurance (VBPI) strategy with the well-known constant proportion portfolio insurance (CPPI) strategy. In this respect, we employ a variety of performance evaluation criteria such as Sharpe, Omega and Kappa ratios to compare the two methods. Our results indicate that the CPPI strategy has a better risk-return tradeoff in most of the scenarios analyzed and maintains a relatively stable return profile for the resulting portfolio at the maturity. ...

Efficient Learning of Nested Deep Hedging using Multiple Options ArXiv ID: 2305.12264 “View on arXiv” Authors: Unknown Abstract Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this setting, the options used as hedging instruments also have to be priced during training. While one might use classical pricing model such as the Black-Scholes formula, ignoring frictions can offer arbitrage opportunities which are undesirable for deep hedging learning. The goal of this study is to develop a nested deep hedging method. That is, we develop a fully-deep approach of deep hedging in which the hedging instruments are also priced by deep neural networks that are aware of frictions. However, since the prices of hedging instruments have to be calculated under many different conditions, the entire learning process can be computationally intractable. To overcome this problem, we propose an efficient learning method for nested deep hedging. Our method consists of three techniques to circumvent computational intractability, each of which reduces redundant computations during training. We show through experiments that the Black-Scholes pricing of hedge instruments can admit significant arbitrage opportunities, which are not observed when the pricing is performed by deep hedging. We also demonstrate that our proposed method successfully reduces the hedging risks compared to a baseline method that does not use options as hedging instruments. ...

Efficient inverse $Z$-transform: sufficient conditions ArXiv ID: 2305.10725 “View on arXiv” Authors: Unknown Abstract We derive several sets of sufficient conditions for applicability of the new efficient numerical realization of the inverse $Z$-transform. For large $n$, the complexity of the new scheme is dozens of times smaller than the complexity of the trapezoid rule. As applications, pricing of European options and single barrier options with discrete monitoring are considered; applications to more general options with barrier-lookback features are outlined. In the case of sectorial transition operators, hence, for symmetric Lévy models, the proof is straightforward. In the case of non-symmetric Lévy models, we construct a non-linear deformation of the dual space, which makes the transition operator sectorial, with an arbitrary small opening angle, and justify the new realization. We impose mild conditions which are satisfied for wide classes of non-symmetric Stieltjes-Lévy processes. ...