Neural Networks

Fast Deep Hedging with Second-Order Optimization ArXiv ID: 2410.22568 “View on arXiv” Authors: Unknown Abstract Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may be delicate and suffer from slow convergence, particularly for options with long maturities and complex sensitivities to market parameters. To address this, we propose a second-order optimization scheme for deep hedging. We leverage pathwise differentiability to construct a curvature matrix, which we approximate as block-diagonal and Kronecker-factored to efficiently precondition gradients. We evaluate our method on a challenging and practically important problem: hedging a cliquet option on a stock with stochastic volatility by trading in the spot and vanilla options. We find that our second-order scheme can optimize the policy in 1/4 of the number of steps that standard adaptive moment-based optimization takes. ...

Constrained portfolio optimization in a life-cycle model ArXiv ID: 2410.20060 “View on arXiv” Authors: Unknown Abstract This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance. ...

Transfer learning for financial data predictions: a systematic review ArXiv ID: 2409.17183 “View on arXiv” Authors: Unknown Abstract Literature highlighted that financial time series data pose significant challenges for accurate stock price prediction, because these data are characterized by noise and susceptibility to news; traditional statistical methodologies made assumptions, such as linearity and normality, which are not suitable for the non-linear nature of financial time series; on the other hand, machine learning methodologies are able to capture non linear relationship in the data. To date, neural network is considered the main machine learning tool for the financial prices prediction. Transfer Learning, as a method aimed at transferring knowledge from source tasks to target tasks, can represent a very useful methodological tool for getting better financial prediction capability. Current reviews on the above body of knowledge are mainly focused on neural network architectures, for financial prediction, with very little emphasis on the transfer learning methodology; thus, this paper is aimed at going deeper on this topic by developing a systematic review with respect to application of Transfer Learning for financial market predictions and to challenges/potential future directions of the transfer learning methodologies for stock market predictions. ...

Deep Gamma Hedging ArXiv ID: 2409.13567 “View on arXiv” Authors: Unknown Abstract We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black–Scholes model then we find the network will successfully learn the Black-Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black–Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs. ...

A deep primal-dual BSDE method for optimal stopping problems ArXiv ID: 2409.06937 “View on arXiv” Authors: Unknown Abstract We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which consists of subnetwork parameterization of a continuation value and spatial gradients from present up to the stopping time. Notable features of the method include: (i) The martingale part in the loss function reduces the variance of stochastic gradients, which facilitates the training of the neural networks as well as alleviates the error propagation of value function approximation; (ii) this martingale approximates the martingale in the Doob-Meyer decomposition, and thus leads to a true upper bound for the optimal value in a non-nested Monte Carlo way. We test the proposed method in American option pricing problems, where the spatial gradient network yields the hedging ratio directly. ...

Advancing Financial Forecasting: A Comparative Analysis of Neural Forecasting Models N-HiTS and N-BEATS ArXiv ID: 2409.00480 “View on arXiv” Authors: Unknown Abstract In the rapidly evolving field of financial forecasting, the application of neural networks presents a compelling advancement over traditional statistical models. This research paper explores the effectiveness of two specific neural forecasting models, N-HiTS and N-BEATS, in predicting financial market trends. Through a systematic comparison with conventional models, this study demonstrates the superior predictive capabilities of neural approaches, particularly in handling the non-linear dynamics and complex patterns inherent in financial time series data. The results indicate that N-HiTS and N-BEATS not only enhance the accuracy of forecasts but also boost the robustness and adaptability of financial predictions, offering substantial advantages in environments that require real-time decision-making. The paper concludes with insights into the practical implications of neural forecasting in financial markets and recommendations for future research directions. ...

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. ...

NeuralBeta: Estimating Beta Using Deep Learning ArXiv ID: 2408.01387 “View on arXiv” Authors: Unknown Abstract Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a novel method using neural networks called NeuralBeta, which is capable of handling both univariate and multivariate scenarios and tracking the dynamic behavior of beta. To address the issue of interpretability, we introduce a new output layer inspired by regularized weighted linear regression, which provides transparency into the model’s decision-making process. We conducted extensive experiments on both synthetic and market data, demonstrating NeuralBeta’s superior performance compared to benchmark methods across various scenarios, especially instances where beta is highly time-varying, e.g., during regime shifts in the market. This model not only represents an advancement in the field of beta estimation, but also shows potential for applications in other financial contexts that assume linear relationships. ...

AI-Powered Energy Algorithmic Trading: Integrating Hidden Markov Models with Neural Networks ArXiv ID: 2407.19858 “View on arXiv” Authors: Unknown Abstract In quantitative finance, machine learning methods are essential for alpha generation. This study introduces a new approach that combines Hidden Markov Models (HMM) and neural networks, integrated with Black-Litterman portfolio optimization. During the COVID period (2019-2022), this dual-model approach achieved a 83% return with a Sharpe ratio of 0.77. It incorporates two risk models to enhance risk management, showing efficiency during volatile periods. The methodology was implemented on the QuantConnect platform, which was chosen for its robust framework and experimental reproducibility. The system, which predicts future price movements, includes a three-year warm-up to ensure proper algorithm function. It targets highly liquid, large-cap energy stocks to ensure stable and predictable performance while also considering broker payments. The dual-model alpha system utilizes log returns to select the optimal state based on the historical performance. It combines state predictions with neural network outputs, which are based on historical data, to generate trading signals. This study examined the architecture of the trading system, data pre-processing, training, and performance. The full code and backtesting data are available under the QuantConnect terms: https://github.com/tiagomonteiro0715/AI-Powered-Energy-Algorithmic-Trading-Integrating-Hidden-Markov-Models-with-Neural-Networks ...

Enhancing Black-Scholes Delta Hedging via Deep Learning ArXiv ID: 2407.19367 “View on arXiv” Authors: Unknown Abstract 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. ...