Mean field equilibrium asset pricing model under partial observation: An exponential quadratic Gaussian approach ArXiv ID: 2410.01352 “View on arXiv” Authors: Unknown Abstract This paper studies an asset pricing model in a partially observable market with a large number of heterogeneous agents using the mean field game theory. In this model, we assume that investors can only observe stock prices and must infer the risk premium from these observations when determining trading strategies. We characterize the equilibrium risk premium in such a market through a solution to the mean field backward stochastic differential equation (BSDE). Specifically, the solution to the mean field BSDE can be expressed semi-analytically by employing an exponential quadratic Gaussian framework. We then construct the risk premium process, which cannot be observed directly by investors, endogenously using the Kalman-Bucy filtering theory. In addition, we include a simple numerical simulation to visualize the dynamics of our market model. ...

Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach ArXiv ID: 2410.01378 “View on arXiv” Authors: Unknown Abstract This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {“Therein, w”}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {“analysis”} for forward investment and consumption under model uncertainty. ...

Worst-case values of target semi-variances with applications to robust portfolio selection ArXiv ID: 2410.01732 “View on arXiv” Authors: Unknown Abstract The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance, and many other fields. Jagannathan (1977) derived the worst-case expected regrets when only the mean and variance of a loss are known and the loss is arbitrary, symmetric, or non-negative. While Chen et al. (2011) obtained the worst-case target semi-variances under similar conditions but focusing on arbitrary losses. In this paper, we first complement the study of Chen et al. (2011) on the worst-case target semi-variances and derive the closed-form expressions for the worst-case target semi-variance when only the mean and variance of a loss are known and the loss is symmetric or non-negative. Then, we investigate worst-case target semi-variances over uncertainty sets that represent undesirable scenarios faced by an investors. Our methods for deriving these worst-case values are different from those used in Jagannathan (1977) and Chen et al. (2011). As applications of the results derived in this paper, we propose robust portfolio selection methods that minimize the worst-case target semi-variance of a portfolio loss over different uncertainty sets. To explore the insights of our robust portfolio selection methods, we conduct numerical experiments with real financial data and compare our portfolio selection methods with several existing portfolio selection models related to the models proposed in this paper. ...

Impermanent loss and loss-vs-rebalancing I: some statistical properties ArXiv ID: 2410.00854 “View on arXiv” Authors: Unknown Abstract There are two predominant metrics to assess the performance of automated market makers and their profitability for liquidity providers: ‘impermanent loss’ (IL) and ’loss-versus-rebalance’ (LVR). In this short paper we shed light on the statistical aspects of both concepts and show that they are more similar than conventionally appreciated. Our analysis uses the properties of a random walk and some analytical properties of the statistical integral combined with the mechanics of a constant function market maker (CFMM). We consider non-toxic or rather unspecific trading in this paper. Our main finding can be summarized in one sentence: For Brownian motion with a given volatility, IL and LVR have identical expectation values but vastly differing distribution functions. ...

KANOP: A Data-Efficient Option Pricing Model using Kolmogorov-Arnold Networks ArXiv ID: 2410.00419 “View on arXiv” Authors: Unknown Abstract Inspired by the recently proposed Kolmogorov-Arnold Networks (KANs), we introduce the KAN-based Option Pricing (KANOP) model to value American-style options, building on the conventional Least Square Monte Carlo (LSMC) algorithm. KANs, which are based on Kolmogorov-Arnold representation theorem, offer a data-efficient alternative to traditional Multi-Layer Perceptrons, requiring fewer hidden layers to achieve a higher level of performance. By leveraging the flexibility of KANs, KANOP provides a learnable alternative to the conventional set of basis functions used in the LSMC model, allowing the model to adapt to the pricing task and effectively estimate the expected continuation value. Using examples of standard American and Asian-American options, we demonstrate that KANOP produces more reliable option value estimates, both for single-dimensional cases and in more complex scenarios involving multiple input variables. The delta estimated by the KANOP model is also more accurate than that obtained using conventional basis functions, which is crucial for effective option hedging. Graphical illustrations further validate KANOP’s ability to accurately model the expected continuation value for American-style options. ...

A Framework for the Construction of a Sentiment-Driven Performance Index: The Case of DAX40 ArXiv ID: 2409.20397 “View on arXiv” Authors: Unknown Abstract We extract the sentiment from german and english news articles on companies in the DAX40 stock market index and use it to create a sentiment-powered pendant. Comparing it to existing products which adjust their weights at pre-defined dates once per month, we show that our index is able to react more swiftly to sentiment information mined from online news. Over the nearly 6 years we considered, the sentiment index manages to create an annualized return of 7.51% compared to the 2.13% of the DAX40, while taking transaction costs into account. In this work, we present the framework we employed to develop this sentiment index. ...

A Hierarchical conv-LSTM and LLM Integrated Model for Holistic Stock Forecasting ArXiv ID: 2410.12807 “View on arXiv” Authors: Unknown Abstract The financial domain presents a complex environment for stock market prediction, characterized by volatile patterns and the influence of multifaceted data sources. Traditional models have leveraged either Convolutional Neural Networks (CNN) for spatial feature extraction or Long Short-Term Memory (LSTM) networks for capturing temporal dependencies, with limited integration of external textual data. This paper proposes a novel Two-Level Conv-LSTM Neural Network integrated with a Large Language Model (LLM) for comprehensive stock advising. The model harnesses the strengths of Conv-LSTM for analyzing time-series data and LLM for processing and understanding textual information from financial news, social media, and reports. In the first level, convolutional layers are employed to identify local patterns in historical stock prices and technical indicators, followed by LSTM layers to capture the temporal dynamics. The second level integrates the output with an LLM that analyzes sentiment and contextual information from textual data, providing a holistic view of market conditions. The combined approach aims to improve prediction accuracy and provide contextually rich stock advising. ...

Computing Systemic Risk Measures with Graph Neural Networks ArXiv ID: 2410.07222 “View on arXiv” Authors: Unknown Abstract This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph structured data. In particular, we focus on an aggregation function that is derived from a market clearing algorithm proposed by Eisenberg and Noe (2001). In this setting, we show the existence of an optimal random allocation that distributes the overall minimal bailout capital and secures the network. We study numerical methods for the approximation of systemic risk and optimal random allocations. We propose to use permutation equivariant architectures of neural networks like graph neural networks (GNNs) and a class that we name (extended) permutation equivariant neural networks ((X)PENNs). We compare their performance to several benchmark allocations. The main feature of GNNs and (X)PENNs is that they are permutation equivariant with respect to the underlying graph data. In numerical experiments we find evidence that these permutation equivariant methods are superior to other approaches. ...

Detecting Structural breakpoints in natural gas and electricity wholesale prices via Bayesian ensemble approach, in the era of energy prices turmoil of 2022 period: the cases of ten European markets ArXiv ID: 2410.07224 “View on arXiv” Authors: Unknown Abstract We investigate the impact of several critical events associated with the Russo Ukrainian war, started officially on 24 February 2022 with the Russian invasion of Ukraine, on ten European electricity markets, two natural gas markets (the European reference trading hub TTF and N.Y. NGNMX market) and how these markets interact to each other and with USDRUB exchange rate, a financial market. We analyze the reactions of these markets, manifested as breakpoints attributed to these critical events, and their interaction, by using a set of three tools that can shed light on different aspects of this complex situation. We combine the concepts of market efficiency, measured by quantifying the Efficient market hypothesis (EMH) via rolling Hurst exponent, with structural breakpoints occurred in the time series of gas, electricity and financial markets, the detection of which is possible by using a Bayesian ensemble approach, the Bayesian Estimator of Abrupt change, Seasonal change and Trend (BEAST), a powerful tool that can effectively detect structural breakpoints, trends, seasonalities and sudden abrupt changes in time series. The results show that the analyzed markets have exhibited different modes of reactions to the critical events, both in respect of number, nature, and time of occurrence (leading, lagging, concurrent with dates of critical events) of breakpoints as well as of the dynamic behavior of their trend components. ...

GARCH-Informed Neural Networks for Volatility Prediction in Financial Markets ArXiv ID: 2410.00288 “View on arXiv” Authors: Unknown Abstract Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE). ...