The problem of hedging derivatives represents a central challenge in financial markets. Under Markovian models, the theory is very well developed, specifically for European-style derivatives. However, significant challenges arise when considering path-dependent options where the payoff depends on the asset's entire price path, or further still, when the underlying asset has non-Markovian dynamics, where conventional parametrized hedging approaches tend to be too restrictive or untractable. In response to these challenges, non-parametric approaches have gained a lot of popularity, and more specifically with the improvement of machine learning software and hardware, deep hedging approaches for their versatility, ease of train and ability to capture nonlinearities, see for instance B uhler et al. (2018).

Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well understood, hindering their real-world applicability. In this research, our aim is to offer actionable insights into the utility of deep PDE solvers for practical option pricing implementation. Through comparative experiments in both the Black--Scholes and the Heston model, we assess the empirical performance of two neural network algorithms to solve PDEs: the Deep Galerkin Method and the Time Deep Gradient Flow method (TDGF). We determine their empirical convergence rates and training time as functions of (i) the number of sampling stages, (ii) the number of samples, (iii) the number of layers, and (iv) the number of nodes per layer. For the TDGF, we also consider the order of the discretization scheme and the number of time steps.

Since the advent of generative artificial intelligence, every company and researcher has been rushing to develop their own generative models, whether commercial or not. Given the large number of users of these powerful new tools, there is currently no intrinsically verifiable way to explain from the ground up what happens when LLMs (large language models) learn. For example, those based on automatic speech recognition systems, which have to rely on huge and astronomical amounts of data collected from all over the web to produce fast and efficient results, In this article, we develop a backdoor attack called MarketBackFinal 2.0, based on acoustic data poisoning, MarketBackFinal 2.0 is mainly based on modern stock market models. In order to show the possible vulnerabilities of speech-based transformers that may rely on LLMs.

This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these residuals, enhancing deep learning performance. Utilizing ten years of daily S&P 500 index option data, our empirical analysis demonstrates that learning the residuals, using the mean squared one-step hedging error as the loss function, significantly improves hedging performance over directly learning the hedging function, often by more than 100%. Adding input features when learning the residuals enhances hedging performance more for puts than calls, with market sentiment being less crucial. Furthermore, learning the residuals with three years of data matches the hedging performance of directly learning with ten years of data, proving that our method demands less data.

Since the advent of the Black and Scholes (1973) framework, dynamic hedging has become a standard financial risk management tool for managing the risk associated with options portfolios. The Black and Scholes (1973) framework has the remarkable property that delta hedging -a hedging strategy invested exclusively in the underlying asset and the money market account-achieves the perfect replication of a European-style contingent claim. In practice, this property is lost due to frictions. Most notably, considering the infrequent rebalancing of the hedging portfolio, classic delta hedging, which is inherently local, can no longer protect against infinitesimal shocks in the underlying asset price. Such an imperfect hedge inevitably yields a hedging error that has to be managed.

Over the past few decades, machine learning models have been extremely successful. As a result of axiomatic attribution methods, feature contributions have been explained more clearly and rigorously. There are, however, few studies that have examined domain knowledge in conjunction with the axioms. In this study, we examine asset pricing in finance, a field closely related to risk management. Consequently, when applying machine learning models, we must ensure that the attribution methods reflect the underlying risks accurately. In this work, we present and study several axioms derived from asset pricing domain knowledge. It is shown that while Shapley value and Integrated Gradients preserve most axioms, neither can satisfy all axioms. Using extensive analytical and empirical examples, we demonstrate how attribution methods can reflect risks and when they should not be used.

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real-world data from the stock options market were used as the initial boundary to solve the Black-Scholes Equation. In particular, times series of call options prices of Brazilian companies Petrobras and Vale were employed. The results indicate that the network can learn to solve the Black-Sholes Equation for a specific real-world stock options time series. The experimental results showed that the Neural network option pricing based on the Black-Sholes Equation solution can reach an option pricing forecasting more accurate than the traditional Black-Sholes analytical solutions. The experimental results making it possible to use this methodology to make short-term call option price forecasts in options markets.

Former House Speaker Nancy Pelosi has invested up to 5 million in a San Francisco-based company, adding to her successful portfolio of Big Tech. Documents revealed Pelosi's transaction with privately held Databricks, which is a software company based on AI technology, took place on March 3 and was disclosed on March 21. Databricks is just the latest newcomer to Pelosi's long list of companies, but there are eight major names that she has invested 16 million in since 2022. While she has not broken any laws by buying and selling stocks, many Americans and other government officials see the investments as conflicts of interest since she has access to confidential intelligence and the power to impact businesses. Documents revealed Pelosi's transaction with privately held Databricks, which is a software company based on AI technology, took place on March 3 and disclosed on March 21 Databricks is just the latest newcomer to Pelosi's long list of companies, but there are eight major names that she has invested up to 16.1 million in since 2022 Databricks, founded in 2013, raised 500 million last year based on a 43 billion valuation.

Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly operations in the algorithms, one of which is preparing a quantum state that encodes a probability distribution of the underlying asset price. In particular, in pricing a path-dependent option, we need to generate a state encoding a joint distribution of the underlying asset price at multiple time points, which is more demanding. To address these issues, we propose a novel approach using Matrix Product State (MPS) as a generative model for time series generation. To validate our approach, taking the Heston model as a target, we conduct numerical experiments to generate time series in the model. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers.

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement Learning (RL) models were recently proposed to tackle this task. However, existing RL works for hedging do not consider market impact caused by the finite liquidity of traded instruments. Integrating such feature can be crucial to achieve optimal performance when hedging options on stocks with limited liquidity. In this paper, we propose a novel general market impact dynamic hedging model based on Deep Reinforcement Learning (DRL) that considers several realistic features such as convex market impacts, and impact persistence through time. The optimal policy obtained from the DRL model is analysed using several option hedging simulations and compared to commonly used procedures such as delta hedging. Results show our DRL model behaves better in contexts of low liquidity by, among others: 1) learning the extent to which portfolio rebalancing actions should be dampened or delayed to avoid high costs, 2) factoring in the impact of features not considered by conventional approaches, such as previous hedging errors through the portfolio value, and the underlying asset's drift (i.e. the magnitude of its expected return).