A simulated electronic market with speculative behaviour and bubble formation ArXiv ID: 2311.12247 “View on arXiv” Authors: Unknown Abstract This paper presents an agent based model of an electronic market with two types of trading agents. One type follows a mean reverting strategy and the other, the speculative trader, tracks the maximum realised return over recent trades. The speculators have a distribution of returns concentrated on negative returns, with a small fraction making profits. The market experiences an increased volatility and prices that greatly depart from the fundamental value of the asset. Our research provides synthetic datasets of the order book to study its dynamics under different levels of speculation ...

Deep State-Space Model for Predicting Cryptocurrency Price ArXiv ID: 2311.14731 “View on arXiv” Authors: Unknown Abstract Our work presents two fundamental contributions. On the application side, we tackle the challenging problem of predicting day-ahead crypto-currency prices. On the methodological side, a new dynamical modeling approach is proposed. Our approach keeps the probabilistic formulation of the state-space model, which provides uncertainty quantification on the estimates, and the function approximation ability of deep neural networks. We call the proposed approach the deep state-space model. The experiments are carried out on established cryptocurrencies (obtained from Yahoo Finance). The goal of the work has been to predict the price for the next day. Benchmarking has been done with both state-of-the-art and classical dynamical modeling techniques. Results show that the proposed approach yields the best overall results in terms of accuracy. ...

Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion ArXiv ID: 2311.12575 “View on arXiv” Authors: Unknown Abstract This paper introduces a novel approach for computing netting–set level and counterparty level exposures, such as Potential Future Exposure (PFE) and Expected Exposure (EE), along with associated sensitivities. The method is essentially an extension of the Fourier-cosine series expansion (COS) method, originally proposed for option pricing. This method can accommodate a broad range of models where the joint distribution of involved risk factors is analytically or semi-analytically tractable. This inclusivity encompasses nearly all CCR models commonly employed in practice. A notable advantage of the COS method is its sustained efficiency, particularly when handling large portfolios. A theoretical error analysis is also provided to justify the method’s theoretical stability and accuracy. Various numerical tests are conducted using real-sized portfolios, and the results underscore its potential as a significantly more efficient alternative to the Monte Carlo method for practical usage, particularly applicable to portfolios involving a relatively modest number of risk factors. Furthermore, the observed error convergence rates align closely with the theoretical error analysis. ...

Generative Machine Learning for Multivariate Equity Returns ArXiv ID: 2311.14735 “View on arXiv” Authors: Unknown Abstract The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization. ...

Hedging carbon risk with a network approach ArXiv ID: 2311.12450 “View on arXiv” Authors: Unknown Abstract Sustainable investing refers to the integration of environmental and social aspects in investors’ decisions. We propose a novel methodology based on the Triangulated Maximally Filtered Graph and node2vec algorithms to construct an hedging portfolio for climate risk, represented by various risk factors, among which the CO2 and the ESG ones. The CO2 factor is strongly correlated consistently over time with the Utility sector, which is the most carbon intensive in the S&P 500 index. Conversely, identifying a group of sectors linked to the ESG factor proves challenging. As a consequence, while it is possible to obtain an efficient hedging portfolio strategy with our methodology for the carbon factor, the same cannot be achieved for the ESG one. The ESG scores appears to be an indicator too broadly defined for market applications. These results support the idea that bank capital requirements should take into account carbon risk. ...

Optimal Portfolio with Ratio Type Periodic Evaluation under Short-Selling Prohibition ArXiv ID: 2311.12517 “View on arXiv” Authors: Unknown Abstract This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our goal is to understand the impact of the periodic reward structure on the long-run constrained portfolio strategy. For power and logarithmic utilities, we can reformulate the original problem into an auxiliary one-period optimization problem. To cope with the auxiliary problem with no short-selling, the dual control problem is introduced and studied, which gives the characterization of the candidate optimal portfolio within one period. With the help of the results from the auxiliary problem, the value function and the optimal constrained portfolio for the original problem with periodic evaluation can be derived and verified, allowing us to discuss some financial implications under the new performance paradigm. ...

Deep Calibration of Market Simulations using Neural Density Estimators and Embedding Networks ArXiv ID: 2311.11913 “View on arXiv” Authors: Unknown Abstract The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in macroeconomic outlook. In recent years, agent-based models have been developed that reproduce many features of an exchange, as summarised by a set of stylised facts and statistics. However, the ability to calibrate simulators to a specific period of trading remains an open challenge. In this work, we develop a novel approach to the calibration of market simulators by leveraging recent advances in deep learning, specifically using neural density estimators and embedding networks. We demonstrate that our approach is able to correctly identify high probability parameter sets, both when applied to synthetic and historical data, and without reliance on manually selected or weighted ensembles of stylised facts. ...

DeFi Security: Turning The Weakest Link Into The Strongest Attraction ArXiv ID: 2312.00033 “View on arXiv” Authors: Unknown Abstract The primary innovation we pioneer – focused on blockchain information security – is called the Safe-House. The Safe-House is badly needed since there are many ongoing hacks and security concerns in the DeFi space right now. The Safe-House is a piece of engineering sophistication that utilizes existing blockchain principles to bring about greater security when customer assets are moved around. The Safe-House logic is easily implemented as smart contracts on any decentralized system. The amount of funds at risk from both internal and external parties – and hence the maximum one time loss – is guaranteed to stay within the specified limits based on cryptographic fundamentals. To improve the safety of the Safe-House even further, we adapt the one time password (OPT) concept to operate using blockchain technology. Well suited to blockchain cryptographic nuances, our secondary advancement can be termed the one time next time password (OTNTP) mechanism. The OTNTP is designed to complement the Safe-House making it even more safe. We provide a detailed threat assessment model – discussing the risks faced by DeFi protocols and the specific risks that apply to blockchain fund management – and give technical arguments regarding how these threats can be overcome in a robust manner. We discuss how the Safe-House can participate with other external yield generation protocols in a secure way. We provide reasons for why the Safe-House increases safety without sacrificing the efficiency of operation. We start with a high level intuitive description of the landscape, the corresponding problems and our solutions. We then supplement this overview with detailed discussions including the corresponding mathematical formulations and pointers for technological implementation. This approach ensures that the article is accessible to a broad audience. ...

Fast and Stable Credit Gamma of CVA ArXiv ID: 2311.11672 “View on arXiv” Authors: Unknown Abstract Credit Valuation Adjustment is a balance sheet item which is nowadays subject to active risk management by specialized traders. However, one of the most important risk factors, which is the vector of default intensities of the counterparty, affects in a non-differentiable way the most general Monte Carlo estimator of the adjustment, through simulation of default times. Thus the computation of first and second order (pure and mixed) sensitivities involving these inputs cannot rely on direct path-wise differentiation, while any approach involving finite differences shows very high statistical noise. We present ad hoc analytical estimators which overcome these issues while offering very low runtime overheads over the baseline computation of the price adjustment. We also discuss the conversion of the so-obtained sensitivities to model parameters (e.g. default intensities) into sensitivities to market quotes (e.g. Credit Default Swap spreads). ...

Optimal Retirement Choice under Age-dependent Force of Mortality ArXiv ID: 2311.12169 “View on arXiv” Authors: Unknown Abstract This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: wealth, labor income, and force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional degenerate optimal stopping problem with interconnected dynamics. We establish the existence of an optimal retirement boundary that splits the state space into continuation and stopping regions. Regularity of the optimal stopping value function is derived and the boundary is proved to be Lipschitz continuous, and it is characterized as the unique solution to a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus retires whenever her wealth exceeds an age-, labor income- and mortality-dependent transformed version of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including the sensitivities of the optimal retirement boundary concerning the relevant model’s parameters. ...