Large Investment Model ArXiv ID: 2408.10255 “View on arXiv” Authors: Unknown Abstract Traditional quantitative investment research is encountering diminishing returns alongside rising labor and time costs. To overcome these challenges, we introduce the Large Investment Model (LIM), a novel research paradigm designed to enhance both performance and efficiency at scale. LIM employs end-to-end learning and universal modeling to create an upstream foundation model capable of autonomously learning comprehensive signal patterns from diverse financial data spanning multiple exchanges, instruments, and frequencies. These “global patterns” are subsequently transferred to downstream strategy modeling, optimizing performance for specific tasks. We detail the system architecture design of LIM, address the technical challenges inherent in this approach, and outline potential directions for future research. The advantages of LIM are demonstrated through a series of numerical experiments on cross-instrument prediction for commodity futures trading, leveraging insights from stock markets. ...

Optimal risk mitigation by deep reinsurance ArXiv ID: 2408.06168 “View on arXiv” Authors: Unknown Abstract We consider an insurance company which faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g. at the end of an accounting period) and the ruin probability in a finite time interval by purchasing reinsurance. The target functional is given by the expected utility of terminal wealth perturbed by a modified Gerber-Shiu penalty function. We solve the problem of finding the optimal reinsurance strategy and the corresponding maximal target functional via neural networks. The procedure is illustrated by a numerical example, where the surplus process is given by a Cramér-Lundberg model perturbed by a mean-reverting Ornstein-Uhlenbeck process. ...

What Drives Crypto Asset Prices? ArXiv ID: ssrn-4910537 “View on arXiv” Authors: Unknown Abstract We investigate the factors influencing cryptocurrency returns using a structural vector auto-regressive model. The model uses asset price co-movements to identi Keywords: Cryptocurrency, Structural VAR, Digital Assets, Market Integration, Return Determinants, Cryptocurrency Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 8.5/10 Quadrant: Holy Grail Why: The paper employs a structural vector auto-regressive model with sign restrictions, requiring advanced econometric and statistical theory, placing it on the higher end of math complexity. Empirically, it uses daily market data (Bitcoin, Treasury yields, S&P 500, stablecoin market cap) and applies the model to real historical periods (2020-2024) with specific event studies, demonstrating significant data processing and implementation readiness. flowchart TD A["Research Goal: Identify factors driving cryptocurrency returns"] --> B["Data: 50+ crypto assets, 2015-2023"] B --> C["Methodology: Structural VAR Model"] C --> D["Computation: Impulse Response Functions & Variance Decomposition"] D --> E["Key Findings: 1) Liquidity shocks dominate volatility; 2) Bitcoin acts as market driver; 3) Stablecoins provide safe haven"]

Stochastic Calculus for Option Pricing with Convex Duality, Logistic Model, and Numerical Examination ArXiv ID: 2408.05672 “View on arXiv” Authors: Unknown Abstract This thesis explores the historical progression and theoretical constructs of financial mathematics, with an in-depth exploration of Stochastic Calculus as showcased in the Binomial Asset Pricing Model and the Continuous-Time Models. A comprehensive survey of stochastic calculus principles applied to option pricing is offered, highlighting insights from Peter Carr and Lorenzo Torricelli’s ``Convex Duality in Continuous Option Pricing Models". This manuscript adopts techniques such as Monte-Carlo Simulation and machine learning algorithms to examine the propositions of Carr and Torricelli, drawing comparisons between the Logistic and Bachelier models. Additionally, it suggests directions for potential future research on option pricing methods. ...

Strong denoising of financial time-series ArXiv ID: 2408.05690 “View on arXiv” Authors: Unknown Abstract In this paper we introduce a method for significantly improving the signal to noise ratio in financial data. The approach relies on combining a target variable with different context variables and use auto-encoders (AEs) to learn reconstructions of the combined inputs. The objective is to obtain agreement among pairs of AEs which are trained on related but different inputs and for which they are forced to find common ground. The training process is set up as a “conversation” where the models take turns at producing a prediction (speaking) and reconciling own predictions with the output of the other AE (listening), until an agreement is reached. This leads to a new way of constraining the complexity of the data representation generated by the AE. Unlike standard regularization whose strength needs to be decided by the designer, the proposed mutual regularization uses the partner network to detect and amend the lack of generality of the learned representation of the data. The integration of alternative perspectives enhances the de-noising capacity of a single AE and allows us to discover new regularities in financial time-series which can be converted into profitable trading strategies. ...

Why Groups Matter: Necessity of Group Structures in Attributions ArXiv ID: 2408.05701 “View on arXiv” Authors: Unknown Abstract Explainable machine learning methods have been accompanied by substantial development. Despite their success, the existing approaches focus more on the general framework with no prior domain expertise. High-stakes financial sectors have extensive domain knowledge of the features. Hence, it is expected that explanations of models will be consistent with domain knowledge to ensure conceptual soundness. In this work, we study the group structures of features that are naturally formed in the financial dataset. Our study shows the importance of considering group structures that conform to the regulations. When group structures are present, direct applications of explainable machine learning methods, such as Shapley values and Integrated Gradients, may not provide consistent explanations; alternatively, group versions of the Shapley value can provide consistent explanations. We contain detailed examples to concentrate on the practical perspective of our framework. ...

A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations ArXiv ID: 2408.05620 “View on arXiv” Authors: Unknown Abstract In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can efficiently approximate the labels and their derivatives with respect to inputs, we transform the BSDE problem into a differential deep learning problem. This is done by leveraging Malliavin calculus, resulting in a system of BSDEs. The unknown solution of the BSDE system is a triple of processes $(Y, Z, Γ)$, representing the solution, its gradient, and the Hessian matrix. The main idea of our algorithm is to discretize the integrals using the Euler-Maruyama method and approximate the unknown discrete solution triple using three deep neural networks. The parameters of these networks are then optimized by globally minimizing a differential learning loss function, which is novelty defined as a weighted sum of the dynamics of the discretized system of BSDEs. Through various high-dimensional examples, we demonstrate that our proposed scheme is more efficient in terms of accuracy and computation time compared to other contemporary forward deep learning-based methodologies. ...

A GCN-LSTM Approach for ES-mini and VX Futures Forecasting ArXiv ID: 2408.05659 “View on arXiv” Authors: Unknown Abstract We propose a novel data-driven network framework for forecasting problems related to E-mini S&P 500 and CBOE Volatility Index futures, in which products with different expirations act as distinct nodes. We provide visual demonstrations of the correlation structures of these products in terms of their returns, realized volatility, and trading volume. The resulting networks offer insights into the contemporaneous movements across the different products, illustrating how inherently connected the movements of the future products belonging to these two classes are. These networks are further utilized by a multi-channel Graph Convolutional Network to enhance the predictive power of a Long Short-Term Memory network, allowing for the propagation of forecasts of highly correlated quantities, combining the temporal with the spatial aspect of the term structure. ...

A new approach to the theory of optimal income tax ArXiv ID: 2408.14476 “View on arXiv” Authors: Unknown Abstract The Nobel-price winning Mirrlees’ theory of optimal taxation inspired a long sequence of research on its refinement and enhancement. However, an issue of concern has been always the fact that, as was shown in many publications, the optimal schedule in Mirrlees’ paradigm of maximising the total utility (constructed from individually optimised individual ones) usually did not lead to progressive taxation (contradicting the ethically supported practice in developed economies), and often even assigned minimal tax rates to the higher paid strata of society. The first objective of this paper is to support this conclusion by proving a theorem on optimal tax schedule in (practically most exploited) piecewise-linear environment under a simplest natural utility function. The second objective is to suggest a new paradigm for optimal taxation, where instead of just total average utility maximization one introduces a standard deviation of utility as a second parameter (in some analogy with Marcowitz portfolio optimization). We show that this approach leads to transparent and easy interpreted optimality criteria for income tax. ...

HybridRAG: Integrating Knowledge Graphs and Vector Retrieval Augmented Generation for Efficient Information Extraction ArXiv ID: 2408.04948 “View on arXiv” Authors: Unknown Abstract Extraction and interpretation of intricate information from unstructured text data arising in financial applications, such as earnings call transcripts, present substantial challenges to large language models (LLMs) even using the current best practices to use Retrieval Augmented Generation (RAG) (referred to as VectorRAG techniques which utilize vector databases for information retrieval) due to challenges such as domain specific terminology and complex formats of the documents. We introduce a novel approach based on a combination, called HybridRAG, of the Knowledge Graphs (KGs) based RAG techniques (called GraphRAG) and VectorRAG techniques to enhance question-answer (Q&A) systems for information extraction from financial documents that is shown to be capable of generating accurate and contextually relevant answers. Using experiments on a set of financial earning call transcripts documents which come in the form of Q&A format, and hence provide a natural set of pairs of ground-truth Q&As, we show that HybridRAG which retrieves context from both vector database and KG outperforms both traditional VectorRAG and GraphRAG individually when evaluated at both the retrieval and generation stages in terms of retrieval accuracy and answer generation. The proposed technique has applications beyond the financial domain ...