arXiv daily: Statistical Finance

arXiv daily: Statistical Finance (q-fin.ST)

1.Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis

Authors:Matthieu Garcin

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.

1.On the Time-Varying Structure of the Arbitrage Pricing Theory using the Japanese Sector Indices

Authors:Koichiro Moriya, Akihiko Noda

Abstract: This paper is the first study to examine the time instability of the APT in the Japanese stock market. In particular, we measure how changes in each risk factor affect the stock risk premiums to investigate the validity of the APT over time, applying the rolling window method to Fama and MacBeth's (1973) two-step regression and Kamstra and Shi's (2023) generalized GRS test. We summarize our empirical results as follows: (1) the APT is supported over the entire sample period but not at all times, (2) the changes in monetary policy greatly affect the validity of the APT in Japan, and (3) the time-varying estimates of the risk premiums for each factor are also unstable over time, and they are affected by the business cycle and economic crises. Therefore, we conclude that the validity of the APT as an appropriate model to explain the Japanese sector index is not stable over time.

1.Deep Stock: training and trading scheme using deep learning

Authors:Sungwoo Kang

Abstract: Despite the efficient market hypothesis, many studies suggest the existence of inefficiencies in the stock market, leading to the development of techniques to gain above-market returns, known as alpha. Systematic trading has undergone significant advances in recent decades, with deep learning emerging as a powerful tool for analyzing and predicting market behavior. In this paper, we propose a model inspired by professional traders that look at stock prices of the previous 600 days and predicts whether the stock price rises or falls by a certain percentage within the next D days. Our model, called DeepStock, uses Resnet's skip connections and logits to increase the probability of a model in a trading scheme. We test our model on both the Korean and US stock markets and achieve a profit of N\% on Korea market, which is M\% above the market return, and profit of A\% on US market, which is B\% above the market return.

1.Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data

Authors:Kyungsub Lee

Abstract: This study examines the use of a recurrent neural network for estimating the parameters of a Hawkes model based on high-frequency financial data, and subsequently, for computing volatility. Neural networks have shown promising results in various fields, and interest in finance is also growing. Our approach demonstrates significantly faster computational performance compared to traditional maximum likelihood estimation methods while yielding comparable accuracy in both simulation and empirical studies. Furthermore, we demonstrate the application of this method for real-time volatility measurement, enabling the continuous estimation of financial volatility as new price data keeps coming from the market.

1.Parameterized Neural Networks for Finance

Authors:Daniel Oeltz, Jan Hamaekers, Kay F. Pilz

Abstract: We discuss and analyze a neural network architecture, that enables learning a model class for a set of different data samples rather than just learning a single model for a specific data sample. In this sense, it may help to reduce the overfitting problem, since, after learning the model class over a larger data sample consisting of such different data sets, just a few parameters need to be adjusted for modeling a new, specific problem. After analyzing the method theoretically and by regression examples for different one-dimensional problems, we finally apply the approach to one of the standard problems asset managers and banks are facing: the calibration of spread curves. The presented results clearly show the potential that lies within this method. Furthermore, this application is of particular interest to financial practitioners, since nearly all asset managers and banks which are having solutions in place may need to adapt or even change their current methodologies when ESG ratings additionally affect the bond spreads.

2.Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies

Authors:Nick James, Max Menzies

Abstract: Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? This paper aims to investigate whether the cryptocurrency market has recently exhibited similarly nuanced mathematical properties as the much more mature equity market. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market, and to what extent.

1.Structured Multifractal Scaling of the Principal Cryptocurrencies: Examination using a Self-Explainable Machine Learning

Authors:Foued Sa√Ędaoui

Abstract: Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural detrended multifractal fluctuation analysis (S-MF-DFA) to investigate the efficiency of the main cryptocurrencies. The new methodology generalizes the conventional approach by allowing it to proceed on the different fluctuation regimes previously determined using a change-points detection test. In this framework, the characterization of the various exogenous factors influencing the scaling behavior is performed on the basis of a single-factor model, thus creating a kind of self-explainable machine learning for price forecasting. The proposal is tested on the daily data of the three among the main cryptocurrencies in order to examine whether the digital market has experienced upheavals in recent years and whether this has in some ways led to a structured multifractal behavior. The sampled period ranges from April 2017 to December 2022. We especially detect common periods of local scaling for the three prices with a decreasing multifractality after 2018. Complementary tests on shuffled and surrogate data prove that the distribution, linear correlation, and nonlinear structure also explain at some level the structural multifractality. Finally, prediction experiments based on neural networks fed with multi-fractionally differentiated data show the interest of this new self-explained algorithm, thus giving decision-makers and investors the ability to use it for more accurate and interpretable forecasts.