Liquidity Dynamics in RFQ Markets and Impact on Pricing ArXiv ID: 2309.04216 “View on arXiv” Authors: Unknown Abstract To assign a value to a portfolio, it is common to use Mark-to-Market prices. However, how should one proceed when the securities are illiquid? When transaction prices are scarce, how can one use all the available real-time information? In this article, we address these questions for over-the-counter (OTC) markets based on requests for quotes (RFQs). We extend the concept of micro-price, which was recently introduced for assets exchanged through limit order books in the market microstructure literature, and incorporate ideas from the recent literature on OTC market making. To account for liquidity imbalances in RFQ markets, we use an approach based on bidimensional Markov-modulated Poisson processes. Beyond extending the concept of micro-price to RFQ markets, we introduce the new concept of Fair Transfer Price. Our concepts of price can be used to value securities fairly, even when the market is relatively illiquid and/or tends to be one-sided. ...

Media Moments and Corporate Connections: A Deep Learning Approach to Stock Movement Classification ArXiv ID: 2309.06559 “View on arXiv” Authors: Unknown Abstract The financial industry poses great challenges with risk modeling and profit generation. These entities are intricately tied to the sophisticated prediction of stock movements. A stock forecaster must untangle the randomness and ever-changing behaviors of the stock market. Stock movements are influenced by a myriad of factors, including company history, performance, and economic-industry connections. However, there are other factors that aren’t traditionally included, such as social media and correlations between stocks. Social platforms such as Reddit, Facebook, and X (Twitter) create opportunities for niche communities to share their sentiment on financial assets. By aggregating these opinions from social media in various mediums such as posts, interviews, and news updates, we propose a more holistic approach to include these “media moments” within stock market movement prediction. We introduce a method that combines financial data, social media, and correlated stock relationships via a graph neural network in a hierarchical temporal fashion. Through numerous trials on current S&P 500 index data, with results showing an improvement in cumulative returns by 28%, we provide empirical evidence of our tool’s applicability for use in investment decisions. ...

Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing ArXiv ID: 2309.04557 “View on arXiv” Authors: Unknown Abstract We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets ${"\cal D"}1,\dots,{"\cal D"}N$ for the same learning model $f_θ$. Our objective is to minimize the cumulative deviation of the generated parameters ${“θ_i(t)"}{“t=0”}^T$ across all $T$ iterations from the specialized parameters $θ^\star{“1”},\ldots,θ^\star_N$ obtained for each dataset, while respecting the loss function for the model $f_{“θ(T)”}$ produced by the algorithm upon halting. We only allow for continual communication between each of the specialized models (nodes/agents) and the central planner (server), at each iteration (round). For the case where the model $f_θ$ is a finite-rank kernel regression, we derive explicit updates for the regret-optimal algorithm. By leveraging symmetries within the regret-optimal algorithm, we further develop a nearly regret-optimal heuristic that runs with $\mathcal{“O”}(Np^2)$ fewer elementary operations, where $p$ is the dimension of the parameter space. Additionally, we investigate the adversarial robustness of the regret-optimal algorithm showing that an adversary which perturbs $q$ training pairs by at-most $\varepsilon>0$, across all training sets, cannot reduce the regret-optimal algorithm’s regret by more than $\mathcal{“O”}(\varepsilon q \bar{“N”}^{“1/2”})$, where $\bar{“N”}$ is the aggregate number of training pairs. To validate our theoretical findings, we conduct numerical experiments in the context of American option pricing, utilizing a randomly generated finite-rank kernel. ...

Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping ArXiv ID: 2309.03984 “View on arXiv” Authors: Unknown Abstract In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our method is substantially enhanced to improve irregularities in the model which are both inherent and induced. Furthermore, the system of coupled PDEs is strongly nonlinear and involves several time-dependent coefficients that include the first-order derivative of the early exercise boundary. These coefficients are approximated from a fourth-order analytical approximation which is derived using a regularized square-root function. The semi-discrete equation for the option value and delta sensitivity is obtained from a non-uniform fourth-order compact finite difference scheme. Fifth-order 5(4) Dormand-Prince time integration method is used to solve the coupled system of discrete equations. Enhancing the performance of our proposed method with local mesh refinement and adaptive strategies enables us to obtain highly accurate solution with very coarse space grids, hence reducing computational runtime substantially. We further verify the performance of our methodology as compared with some of the well-known and better-performing existing methods. ...

Fourier Neural Network Approximation of Transition Densities in Finance ArXiv ID: 2309.03966 “View on arXiv” Authors: Unknown Abstract This paper introduces FourNet, a novel single-layer feed-forward neural network (FFNN) method designed to approximate transition densities for which closed-form expressions of their Fourier transforms, i.e. characteristic functions, are available. A unique feature of FourNet lies in its use of a Gaussian activation function, enabling exact Fourier and inverse Fourier transformations and drawing analogies with the Gaussian mixture model. We mathematically establish FourNet’s capacity to approximate transition densities in the $L_2$-sense arbitrarily well with finite number of neurons. The parameters of FourNet are learned by minimizing a loss function derived from the known characteristic function and the Fourier transform of the FFNN, complemented by a strategic sampling approach to enhance training. We derive practical bounds for the $L_2$ estimation error and the potential pointwise loss of nonnegativity in FourNet for $d$-dimensions ($d\ge 1$), highlighting its robustness and applicability in practical settings. FourNet’s accuracy and versatility are demonstrated through a wide range of dynamics common in quantitative finance, including Lévy processes and the Heston stochastic volatility models-including those augmented with the self-exciting Queue-Hawkes jump process. ...

TradingGPT: Multi-Agent System with Layered Memory and Distinct Characters for Enhanced Financial Trading Performance ArXiv ID: 2309.03736 “View on arXiv” Authors: Unknown Abstract Large Language Models (LLMs), prominently highlighted by the recent evolution in the Generative Pre-trained Transformers (GPT) series, have displayed significant prowess across various domains, such as aiding in healthcare diagnostics and curating analytical business reports. The efficacy of GPTs lies in their ability to decode human instructions, achieved through comprehensively processing historical inputs as an entirety within their memory system. Yet, the memory processing of GPTs does not precisely emulate the hierarchical nature of human memory. This can result in LLMs struggling to prioritize immediate and critical tasks efficiently. To bridge this gap, we introduce an innovative LLM multi-agent framework endowed with layered memories. We assert that this framework is well-suited for stock and fund trading, where the extraction of highly relevant insights from hierarchical financial data is imperative to inform trading decisions. Within this framework, one agent organizes memory into three distinct layers, each governed by a custom decay mechanism, aligning more closely with human cognitive processes. Agents can also engage in inter-agent debate. In financial trading contexts, LLMs serve as the decision core for trading agents, leveraging their layered memory system to integrate multi-source historical actions and market insights. This equips them to navigate financial changes, formulate strategies, and debate with peer agents about investment decisions. Another standout feature of our approach is to equip agents with individualized trading traits, enhancing memory diversity and decision robustness. These sophisticated designs boost the system’s responsiveness to historical trades and real-time market signals, ensuring superior automated trading accuracy. ...

An Offline Learning Approach to Propagator Models ArXiv ID: 2309.02994 “View on arXiv” Authors: Unknown Abstract We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy. ...

GPT-InvestAR: Enhancing Stock Investment Strategies through Annual Report Analysis with Large Language Models ArXiv ID: 2309.03079 “View on arXiv” Authors: Unknown Abstract Annual Reports of publicly listed companies contain vital information about their financial health which can help assess the potential impact on Stock price of the firm. These reports are comprehensive in nature, going up to, and sometimes exceeding, 100 pages. Analysing these reports is cumbersome even for a single firm, let alone the whole universe of firms that exist. Over the years, financial experts have become proficient in extracting valuable information from these documents relatively quickly. However, this requires years of practice and experience. This paper aims to simplify the process of assessing Annual Reports of all the firms by leveraging the capabilities of Large Language Models (LLMs). The insights generated by the LLM are compiled in a Quant styled dataset and augmented by historical stock price data. A Machine Learning model is then trained with LLM outputs as features. The walkforward test results show promising outperformance wrt S&P500 returns. This paper intends to provide a framework for future work in this direction. To facilitate this, the code has been released as open source. ...

On the Impact of Feeding Cost Risk in Aquaculture Valuation and Decision Making ArXiv ID: 2309.02970 “View on arXiv” Authors: Unknown Abstract We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model. We compare the decision of harvesting salmon using a decision rule assuming either deterministic or stochastic feeding costs, i.e. including feeding cost risk. We identify cases, where accounting for stochastic feeding costs leads to significant improvements as well as cases where deterministic feeding costs are a good enough proxy. Nevertheless, in all of these cases, the newly derived rules show superior performance, while the additional computational costs are negligible. From a methodological point of view, we demonstrate how to use Deep-Neural-Networks to infer on the decision boundary that determines harvesting or continuation, improving on more classical regression-based and curve-fitting methods. To achieve this we use a deep classifier, which not only improves on previous results but also scales well for higher dimensional problems, and in addition mitigates effects due to model uncertainty, which we identify in this article. effects due to model uncertainty, which we identify in this article. ...

Exploiting Unfair Advantages: Investigating Opportunistic Trading in the NFT Market ArXiv ID: 2310.06844 “View on arXiv” Authors: Unknown Abstract As cryptocurrency evolved, new financial instruments, such as lending and borrowing protocols, currency exchanges, fungible and non-fungible tokens (NFT), staking and mining protocols have emerged. A financial ecosystem built on top of a blockchain is supposed to be fair and transparent for each participating actor. Yet, there are sophisticated actors who turn their domain knowledge and market inefficiencies to their strategic advantage; thus extracting value from trades not accessible to others. This situation is further exacerbated by the fact that blockchain-based markets and decentralized finance (DeFi) instruments are mostly unregulated. Though a large body of work has already studied the unfairness of different aspects of DeFi and cryptocurrency trading, the economic intricacies of non-fungible token (NFT) trades necessitate further analysis and academic scrutiny. The trading volume of NFTs has skyrocketed in recent years. A single NFT trade worth over a million US dollars, or marketplaces making billions in revenue is not uncommon nowadays. While previous research indicated the presence of wrongdoings in the NFT market, to our knowledge, we are the first to study predatory trading practices, what we call opportunistic trading, in depth. Opportunistic traders are sophisticated actors who employ automated, high-frequency NFT trading strategies, which, oftentimes, are malicious, deceptive, or, at the very least, unfair. Such attackers weaponize their advanced technical knowledge and superior understanding of DeFi protocols to disrupt trades of unsuspecting users, and collect profits from economic situations that are inaccessible to ordinary users, in a “supposedly” fair market. In this paper, we explore three such broad classes of opportunistic strategies aiming to realize three distinct trading objectives, viz., acquire, instant profit generation, and loss minimization. ...