Deep learning for quadratic hedging in incomplete jump market ArXiv ID: 2407.13688 “View on arXiv” Authors: Unknown Abstract We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale measure through the means of the Stackelberg game approach. A deep learning algorithm based on the combination of the feedforward and LSTM neural networks is tested on three different market models, two of which are incomplete. In contrast, the complete market Black-Scholes model serves as a benchmark for the algorithm’s performance. The results that indicate the algorithm’s good performance are presented and discussed. In particular, we apply our results to the special incomplete market model studied by Merton and give a detailed comparison between our results based on the minimal variance principle and the results obtained by Merton based on a different pricing principle. Using deep learning, we find that the minimal variance principle leads to typically higher option prices than those deduced from the Merton principle. On the other hand, the minimal variance principle leads to lower losses than the Merton principle. ...

Deep reinforcement learning with positional context for intraday trading ArXiv ID: 2406.08013 “View on arXiv” Authors: Unknown Abstract Deep reinforcement learning (DRL) is a well-suited approach to financial decision-making, where an agent makes decisions based on its trading strategy developed from market observations. Existing DRL intraday trading strategies mainly use price-based features to construct the state space. They neglect the contextual information related to the position of the strategy, which is an important aspect given the sequential nature of intraday trading. In this study, we propose a novel DRL model for intraday trading that introduces positional features encapsulating the contextual information into its sparse state space. The model is evaluated over an extended period of almost a decade and across various assets including commodities and foreign exchange securities, taking transaction costs into account. The results show a notable performance in terms of profitability and risk-adjusted metrics. The feature importance results show that each feature incorporating contextual information contributes to the overall performance of the model. Additionally, through an exploration of the agent’s intraday trading activity, we unveil patterns that substantiate the effectiveness of our proposed model. ...

HARd to Beat: The Overlooked Impact of Rolling Windows in the Era of Machine Learning ArXiv ID: 2406.08041 “View on arXiv” Authors: Unknown Abstract We investigate the predictive abilities of the heterogeneous autoregressive (HAR) model compared to machine learning (ML) techniques across an unprecedented dataset of 1,455 stocks. Our analysis focuses on the role of fitting schemes, particularly the training window and re-estimation frequency, in determining the HAR model’s performance. Despite extensive hyperparameter tuning, ML models fail to surpass the linear benchmark set by HAR when utilizing a refined fitting approach for the latter. Moreover, the simplicity of HAR allows for an interpretable model with drastically lower computational costs. We assess performance using QLIKE, MSE, and realized utility metrics, finding that HAR consistently outperforms its ML counterparts when both rely solely on realized volatility and VIX as predictors. Our results underscore the importance of a correctly specified fitting scheme. They suggest that properly fitted HAR models provide superior forecasting accuracy, establishing robust guidelines for their practical application and use as a benchmark. This study not only reaffirms the efficacy of the HAR model but also provides a critical perspective on the practical limitations of ML approaches in realized volatility forecasting. ...

Heterogeneous Beliefs Model of Stock Market Predictability ArXiv ID: 2406.08448 “View on arXiv” Authors: Unknown Abstract This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset’s fundamental value through a noisy signal. The investors are heterogeneous in that they have different beliefs about the stochastic supply. A momentum in the stock price arises from those agents who incorrectly underestimate the signal accuracy, dampening the initial price impact of the signal. A reversal in price occurs because the price reverts to the fundamental value in the long run. An extension of the model to multiple assets case predicts co-movement and lead-lag effect, in addition to cross-sectional momentum and reversal. The heterogeneous beliefs of investors about news demonstrate how the main predictability anomalies arise endogenously in a model of bounded rationality. ...

Modeling a Financial System with Memory via Fractional Calculus and Fractional Brownian Motion ArXiv ID: 2406.19408 “View on arXiv” Authors: Unknown Abstract Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the system. In this project, we describe and analyze a financial model based on the fractional Langevin equation with colored noise generated by fractional Brownian motion. Physics-based methods of analysis are used to examine the phase behavior and dispersion relations of the system upon varying input parameters. A type of anomalous marginal glass phase is potentially seen in some regions, which motivates further exploration of this model and expanded use of phase behavior and dispersion relation methods to analyze financial models. ...

A Multi-step Approach for Minimizing Risk in Decentralized Exchanges ArXiv ID: 2406.07200 “View on arXiv” Authors: Unknown Abstract Decentralized Exchanges are becoming even more predominant in today’s finance. Driven by the need to study this phenomenon from an academic perspective, the SIAG/FME Code Quest 2023 was announced. Specifically, participating teams were asked to implement, in Python, the basic functions of an Automated Market Maker and a liquidity provision strategy in an Automated Market Maker to minimize the Conditional Value at Risk, a critical measure of investment risk. As the competition’s winning team, we highlight our approach in this work. In particular, as the dependence of the final return on the initial wealth distribution is highly non-linear, we cannot use standard ad-hoc approaches. Additionally, classical minimization techniques would require a significant computational load due to the cost of the target function. For these reasons, we propose a three-step approach. In the first step, the target function is approximated by a Kernel Ridge Regression. Then, the approximating function is minimized. In the final step, the previously discovered minimum is utilized as the starting point for directly optimizing the desired target function. By using this procedure, we can both reduce the computational complexity and increase the accuracy of the solution. Finally, the overall computational load is further reduced thanks to an algorithmic trick concerning the returns simulation and the usage of Cython. ...

Interconnected Markets: Exploring the Dynamic Relationship Between BRICS Stock Markets and Cryptocurrency ArXiv ID: 2406.07641 “View on arXiv” Authors: Unknown Abstract This study aims to examine the intricate dynamics between BRICS traditional stock assets and the evolving landscape of cryptocurrencies. Using a time-varying parameter vector autoregression model (TVP-VAR), we have analyzed data from the BRICS stock market index, cryptocurrencies, and indicators from January 6, 2015, to June 29, 2023. The results show that three out of the five BRICS stock markets serve as primary sources of shocks that subsequently affect the financial network. The transcontinental (TCI) value derived from the dynamic conditional connectedness using the TVP-VAR model demonstrates a higher explanatory power than the static connectedness observed using the standard VAR model. The discoveries from this study offer valuable insights for corporations, investors, and regulators concerning systematic risk and investment strategies. ...

Probabilistic models and statistics for electronic financial markets in the digital age ArXiv ID: 2406.07388 “View on arXiv” Authors: Unknown Abstract The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation. ...

The Theory of Intrinsic Time: A Primer ArXiv ID: 2406.07354 “View on arXiv” Authors: Unknown Abstract The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was first introduced. This paper expands on this theme by discussing the paradigm of intrinsic time, its origins, history, and modern applications. Departing from traditional, continuous measures of time, intrinsic time proposes an event-based, algorithmic framework that captures the dynamic and fluctuating nature of real-world phenomena more accurately. Unsuspected implications arise in general for complex systems and specifically for financial markets. For instance, novel structures and regularities are revealed, otherwise obscured by any analysis utilizing equidistant time intervals. Of particular interest is the emergence of a multiplicity of scaling laws, a hallmark signature of an underlying organizational principle in complex systems. Moreover, a central insight from this novel paradigm is the realization that universal time does not exist; instead, time is observer-dependent, shaped by the intrinsic activity unfolding within complex systems. This research opens up new avenues for economic modeling and forecasting, paving the way for a deeper understanding of the invisible forces that guide the evolution and emergence of market dynamics and financial systems. An exciting and rich landscape of possibilities emerges within the paradigm of intrinsic time. ...

Application of Black-Litterman Bayesian in Statistical Arbitrage ArXiv ID: 2406.06706 “View on arXiv” Authors: Unknown Abstract \begin{“abstract”} In this paper, we integrated the statistical arbitrage strategy, pairs trading, into the Black-Litterman model and constructed efficient mean-variance portfolios. Typically, pairs trading underperforms under volatile or distressed market condition because the selected asset pairs fail to revert to equilibrium within the investment horizon. By enhancing this strategy with the Black-Litterman portfolio optimization, we achieved superior performance compared to the S&P 500 market index under both normal and extreme market conditions. Furthermore, this research presents an innovative idea of incorporating traditional pairs trading strategies into the portfolio optimization framework in a scalable and systematic manner. ...