Enhancing Financial Data Visualization for Investment Decision-Making ArXiv ID: 2403.18822 “View on arXiv” Authors: Unknown Abstract Navigating the intricate landscape of financial markets requires adept forecasting of stock price movements. This paper delves into the potential of Long Short-Term Memory (LSTM) networks for predicting stock dynamics, with a focus on discerning nuanced rise and fall patterns. Leveraging a dataset from the New York Stock Exchange (NYSE), the study incorporates multiple features to enhance LSTM’s capacity in capturing complex patterns. Visualization of key attributes, such as opening, closing, low, and high prices, aids in unraveling subtle distinctions crucial for comprehensive market understanding. The meticulously crafted LSTM input structure, inspired by established guidelines, incorporates both price and volume attributes over a 25-day time step, enabling the model to capture temporal intricacies. A comprehensive methodology, including hyperparameter tuning with Grid Search, Early Stopping, and Callback mechanisms, leads to a remarkable 53% improvement in predictive accuracy. The study concludes with insights into model robustness, contributions to financial forecasting literature, and a roadmap for real-time stock market prediction. The amalgamation of LSTM networks, strategic hyperparameter tuning, and informed feature selection presents a potent framework for advancing the accuracy of stock price predictions, contributing substantively to financial time series forecasting discourse. ...

Deep Learning for Dynamic NFT Valuation ArXiv ID: 2312.05346 “View on arXiv” Authors: Unknown Abstract I study the price dynamics of non-fungible tokens (NFTs) and propose a deep learning framework for dynamic valuation of NFTs. I use data from the Ethereum blockchain and OpenSea to train a deep learning model on historical trades, market trends, and traits/rarity features of Bored Ape Yacht Club NFTs. After hyperparameter tuning, the model is able to predict the price of NFTs with high accuracy. I propose an application framework for this model using zero-knowledge machine learning (zkML) and discuss its potential use cases in the context of decentralized finance (DeFi) applications. ...

Efficient evaluation of joint pdf of a Lévy process, its extremum, and hitting time of the extremum ArXiv ID: 2312.05222 “View on arXiv” Authors: Unknown Abstract For Lévy processes with exponentially decaying tails of the Lévy density, we derive integral representations for the joint cpdf $V$ of $(X_T, \bar X_T,τ_T)$ (the process, its supremum evaluated at $T<+\infty$, and the first time at which $X$ attains its supremum). The first representation is a Riemann-Stieltjes integral in terms of the (cumulative) probability distribution of the supremum process and joint probability distribution function of the process and its supremum process. The integral is evaluated using a combination an analog of the trapezoid rule. The second representation is amenable to more accurate albeit slower calculations. We calculate explicitly the Laplace-Fourier transform of $V$ w.r.t. all arguments, apply the inverse transforms, and reduce the problem to evaluation of the sum of 5D integrals. The integrals can be evaluated using the summation by parts in the infinite trapezoid rule and simplified trapezoid rule; the inverse Laplace transforms can be calculated using the Gaver-Wynn-Rho algorithm. Under additional conditions on the domain of analyticity of the characteristic exponent, the speed of calculations is greatly increased using the conformal deformation technique. For processes of infinite variation, the program in Matlab running on a Mac with moderate characteristics achieves the precision better than E-05 in a fraction of a second; the precision better than E-10 is achievable in dozens of seconds. As the order of the process (the analog of the Blumenthal-Getoor index) decreases, the CPU time increases, and the best accuracy achievable with double precision arithmetic decreases. ...

Onflow: an online portfolio allocation algorithm ArXiv ID: 2312.05169 “View on arXiv” Authors: Unknown Abstract We introduce Onflow, a reinforcement learning technique that enables online optimization of portfolio allocation policies based on gradient flows. We devise dynamic allocations of an investment portfolio to maximize its expected log return while taking into account transaction fees. The portfolio allocation is parameterized through a softmax function, and at each time step, the gradient flow method leads to an ordinary differential equation whose solutions correspond to the updated allocations. This algorithm belongs to the large class of stochastic optimization procedures; we measure its efficiency by comparing our results to the mathematical theoretical values in a log-normal framework and to standard benchmarks from the ‘old NYSE’ dataset. For log-normal assets, the strategy learned by Onflow, with transaction costs at zero, mimics Markowitz’s optimal portfolio and thus the best possible asset allocation strategy. Numerical experiments from the ‘old NYSE’ dataset show that Onflow leads to dynamic asset allocation strategies whose performances are: a) comparable to benchmark strategies such as Cover’s Universal Portfolio or Helmbold et al. “multiplicative updates” approach when transaction costs are zero, and b) better than previous procedures when transaction costs are high. Onflow can even remain efficient in regimes where other dynamical allocation techniques do not work anymore. Therefore, as far as tested, Onflow appears to be a promising dynamic portfolio management strategy based on observed prices only and without any assumption on the laws of distributions of the underlying assets’ returns. In particular it could avoid model risk when building a trading strategy. ...

A General Framework for Portfolio Construction Based on Generative Models of Asset Returns ArXiv ID: 2312.03294 “View on arXiv” Authors: Unknown Abstract In this paper, we present an integrated approach to portfolio construction and optimization, leveraging high-performance computing capabilities. We first explore diverse pairings of generative model forecasts and objective functions used for portfolio optimization, which are evaluated using performance-attribution models based on LASSO. We illustrate our approach using extensive simulations of crypto-currency portfolios, and we show that the portfolios constructed using the vine-copula generative model and the Sharpe-ratio objective function consistently outperform. To accommodate a wide array of investment strategies, we further investigate portfolio blending and propose a general framework for evaluating and combining investment strategies. We employ an extension of the multi-armed bandit framework and use value models and policy models to construct eclectic blended portfolios based on past performance. We consider similarity and optimality measures for value models and employ probability-matching (“blending”) and a greedy algorithm (“switching”) for policy models. The eclectic portfolios are also evaluated using LASSO models. We show that the value model utilizing cosine similarity and logit optimality consistently delivers robust superior performances. The extent of outperformance by eclectic portfolios over their benchmarks significantly surpasses that achieved by individual generative model-based portfolios over their respective benchmarks. ...

Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models ArXiv ID: 2312.03915 “View on arXiv” Authors: Unknown Abstract We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates. ...

Simulation of a Lévy process, its extremum, and hitting time of the extremum via characteristic functions ArXiv ID: 2312.03929 “View on arXiv” Authors: Unknown Abstract We suggest a general framework for simulation of the triplet $(X_T,\bar X_ T,τ_T)$ (Lévy process, its extremum, and hitting time of the extremum), and, separately, $X_T,\bar X_ T$ and pairs $(X_T,\bar X_ T)$, $(\bar X_ T,τ_T)$, $(\bar X_ T-X_T,τ_T)$, via characteristic functions and conditional characteristic functions. The conformal deformations technique allows one to evaluate probability distributions, joint probability distributions and conditional probability distributions accurately and fast. For simulations in the far tails of the distribution, we precalculate and store the values of the (conditional) characteristic functions on multi-grids on appropriate surfaces in $C^n$, and use these values to calculate the quantiles in the tails. For simulation in the central part of a distribution, we precalculate the values of the cumulative distribution at points of a non-uniform (multi-)grid, and use interpolation to calculate quantiles. ...

The Mean Field Market Model Revisited ArXiv ID: 2402.10215 “View on arXiv” Authors: Unknown Abstract In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate’s variances over large time horizons. This maintains the market model’s practicability, since calibrations and simulations can be carried out efficiently without nested simulations. In addition, we show that our framework can be directly applied to model term rates derived from SOFR, ESTR or other nearly risk-free overnight short-term rates – a crucial feature since many IBOR rates are gradually being replaced. These results are complemented by a calibration study and some theoretical arguments which allow to estimate the probability of unrealistically high rates in the presented market models. ...

Towards Sobolev Pruning ArXiv ID: 2312.03510 “View on arXiv” Authors: Unknown Abstract The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo simulation. The predominant approach of fitting a large neural network and then pruning it to a reduced size has commonly neglected shortcomings. The produced surrogate models often will not capture the sensitivities and uncertainties inherent in the original model. In particular, (higher-order) derivative information of such surrogates could differ drastically. Given a large enough network, we expect this derivative information to match. However, the pruned model will almost certainly not share this behavior. In this paper, we propose to find surrogate models by using sensitivity information throughout the learning and pruning process. We build on work using Interval Adjoint Significance Analysis for pruning and combine it with the recent advancements in Sobolev Training to accurately model the original sensitivity information in the pruned neural network based surrogate model. We experimentally underpin the method on an example of pricing a multidimensional Basket option modelled through a stochastic differential equation with Brownian motion. The proposed method is, however, not limited to the domain of quantitative finance, which was chosen as a case study for intuitive interpretations of the sensitivities. It serves as a foundation for building further surrogate modelling techniques considering sensitivity information. ...

An explanation for the distribution characteristics of stock returns ArXiv ID: 2312.02472 “View on arXiv” Authors: Unknown Abstract Observations indicate that the distributions of stock returns in financial markets usually do not conform to normal distributions, but rather exhibit characteristics of high peaks, fat tails and biases. In this work, we assume that the effects of events or information on prices obey normal distribution, while financial markets often overreact or underreact to events or information, resulting in non normal distributions of stock returns. Based on the above assumptions, we propose a reaction function for a financial market reacting to events or information, and a model based on it to describe the distribution of real stock returns. Our analysis of the returns of China Securities Index 300 (CSI 300), the Standard & Poor’s 500 Index (SPX or S&P 500) and the Nikkei 225 Index (N225) at different time scales shows that financial markets often underreact to events or information with minor impacts, overreact to events or information with relatively significant impacts, and react slightly stronger to positive events or information than to negative ones. In addition, differences in financial markets and time scales of returns can also affect the shapes of the reaction functions. ...