Financial Market Model Research Articles

On Properties of the Hyperbolic Distribution

This paper is set to analytically describe properties of the hyperbolic distribution. This law, along with the variance-gamma distribution, is one of the most popular normal mean–variance mixtures from the point of view of various applications. We have found closed form expressions for the cumulative distribution and partial-moment-generating functions of the hyperbolic distribution. The obtained formulas use the values of the Humbert confluent hypergeometric and Whittaker special functions. The results are applied to the problem of European option pricing in the related Lévy model of financial market. The research demonstrates that the discussed normal mean–variance mixture is analytically tractable.

Neural Networks and the Nonlinear Feynman–Kac Theorem Applied to Financial Options Pricing

The classic financial market model proposed by Black and Scholes allows solving, under a series of simplifying assumptions, the problem of valuing financial derivatives. However, these assumptions deviate from the reality of global markets, particularly assuming perfect liquidity. In this work, a financial market model is proposed in which the illiquidity of the risky asset is stochastic, described by a mean-reversion process. The dynamics of the asset price in this context are established alongside the valuation PDE for derivatives. Additionally, as an approximation method to the solution of this PDE, the implementation of the extension of the Feynman–Kac representation theorem to the nonlinear case using deep neural networks is proposed.

American option in a market generated by interactive agents

This study introduces a new financial market model inspired by Remita and Eisele's methodology, incorporating a substantial number of interacting agents denoted by “n”. Focusing on the valuation of European and American options within this vast network of agents, and more specifically on behavior when “n” tends to infinity, the research illustrates the convergence of an initially incomplete market towards completeness. In addition, the study scrutinizes the price stability of options on the underlying risky asset, St, in the context of an increasing number of agents. Taking into account a comprehensive set of internal and external factors influencing market dynamics, this study offers a holistic analysis of option price dynamics and market completeness. By examining the complex interactions between a large number of agents and option pricing, the research provides valuable insights into the complexity of financial markets. The results not only elucidate convergence phenomena within an expanding network of agents, they also shed light on the stability of option prices under ever-changing market conditions. This comprehensive analysis underlines the multifaceted nature of financial markets, highlighting the intrinsic relationship between option price dynamics and various market influences. Overall, this study makes a significant contribution to the understanding of financial market dynamics, particularly in the context of option pricing.

Application of Stochastic Processes in Financial Market Models

This paper explores the significant role of stochastic processes in financial modeling, tracing the evolution from basic Brownian motion to sophisticated stochastic differential equations used in modern financial markets. Beginning with the historical development of Brownian motion, identified by Robert Brown and later mathematically modeled by Louis Bachelier for stock price fluctuations, the paper outlines its foundational influence on the Efficient Market Hypothesis and the random walk theory. The extension of these concepts in the Black-Scholes model for option pricing highlights the practical applications of these theories in predicting financial outcomes. The discussion progresses to geometric Brownian motion (GBM) and its crucial role in stock price modeling, emphasizing its use in Monte Carlo simulations for option pricing. The limitations of the Black-Scholes model and GBM in dealing with real market conditions such as stochastic volatility and jump-diffusion processes are addressed, showcasing the evolution of more complex models like the Heston model and GARCH. Interest rate models like the Vasicek and Cox-Ingersoll-Ross models are evaluated for their real-world applicability, particularly in scenarios of low and negative interest rates. This comprehensive review not only underscores the theoretical advancements in financial modeling but also its practical implications in contemporary financial markets.

Asset pricing and hedging in financial markets with fixed and proportional transaction costs

We establish the asset pricing and hedging principle in a financial market model, which is a specific case of the von Neumann-Gale dynamical system, with both fixed and proportional transaction costs and trading constraints. The main results are hedging criteria stated in terms of consistent valuation systems, generalizing the notion of an equivalent martingale measure.

Task-oriented machine learning surrogates for tipping points of agent-based models

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

Disposition effect and its outcome on endogenous price fluctuations

AbstractWe have developed a financial market model that incorporates the Disposition Effect, which refers to traders’ tendency to avoid realizing losses. Specifically, our model replicates several stylized facts commonly observed in financial markets, such as fat tails and volatility clustering. These market characteristics can be attributed to the Disposition Effect, especially when the trading behavior of agents aligns with the findings of Ben-David and Hirshleifer (Rev Financ Stud 25(8):2485–2532, 2012). To demonstrate this, we examine two versions of the model: one where a class of agents exhibits a high degree of Disposition Effect and another where traders are not influenced by it. By comparing the simulated time series generated by both versions, we find that the one with agents affected by the Disposition Effect better replicates the features observed in real financial markets. This holds true for both the deterministic and stochastic versions of the model.

The Financial Market of Indices of Socioeconomic Well-Being

This study discusses how financial economic theory and its quantitative tools can be applied to create socioeconomic indices and develop a financial market for the so-called “socioeconomic well-being indices”. In this study, we quantify socioeconomic well-being by assigning a dollar value to the well-being factors of selected countries; this is analogous to how the Dow 30 encapsulates the financial health of the US market. While environmental, social, and governance (ESG) financial markets address socioeconomic issues, our focus is broader, encompassing national citizens’ well-being. The dollar-denominated socioeconomic indices for each country can be viewed as financial assets that can serve as risky assets for constructing a global index, which, in turn, serves as a “market of well-being socioeconomic index”. This novel global index of well-being, paralleling the Dow Jones Industrial Average (DJIA), provides a comprehensive representation of the world’s socioeconomic status. Through advanced financial econometrics and dynamic asset pricing methodologies, we evaluate the potential for significant downturns in both the socioeconomic well-being indices of individual countries and the aggregate global index. This innovative approach allows us to engineer financial instruments akin to portfolio insurance, such as index puts, designed to hedge against these downturn risks. Our findings propose a financial market model for well-being indices, encouraging the financial industry to adopt and trade these indices as mechanisms to manage and hedge against downturn risks in well-being.

Regular and chaotic dynamics in a 2D discontinuous financial market model with heterogeneous traders

We develop a financial market model where three types of traders operate simultaneously: fundamentalists and chartists of two types, namely, trend followers and contrarians. The dynamics of this model is described by a two-dimensional discontinuous map defined by two linear functions, where one acts in the partition between two (parallel) discontinuity lines and the other one acts outside this partition. Our analysis shows that despite the linearity of the map components, its dynamics can be quite complex, with various, possibly coexisting attracting cycles and chaotic attractors. As a first step towards the understanding how the overall bifurcation structure observed in the parameter space of the map is organized, we obtain analytically the boundaries of periodicity regions related to the simplest attracting period-n cycles, n≥3, with one point in the middle partition and n−1 points outside it. These boundaries can be related to border-collision bifurcations (when a point of the cycle collides with a discontinuity line) as well as to degenerate bifurcations (associated with eigenvalues on the unit circle). We show also some elements of period-adding and period-incrementing bifurcation structures for which the cycles mentioned above are basic. From an economic point of view, our study confirms that a fairly simple financial market model with heterogeneous agents is able to produce complicated boom-bust dynamics typical of real financial markets.

Arbitrage problems with reflected geometric Brownian motion

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation

Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation

A simple learning agent interacting with an agent-based market model

We consider the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event-driven agent-based financial market model. Trading takes place asynchronously through a matching engine in event time. The optimal execution agent is considered at different levels of initial order sizes and differently sized state spaces. The resulting impact on the agent-based model and market is considered using a calibration approach that explores changes in the empirical stylised facts and price impact curves. Convergence, volume trajectory and action trace plots are used to visualise the learning dynamics. The smaller state space agents had the number of states they visited converge much faster than the larger state space agents, and they were able to start learning to trade intuitively using the spread and volume states. We find that the moments of the model are robust to the impact of the learning agents, except for the Hurst exponent, which was lowered by the introduction of strategic order-splitting. The introduction of the learning agent preserves the shape of the price impact curves but can reduce the trade-sign auto-correlations and increase the micro-price volatility when the trading volumes increase.

Innovation and knowledge coordinates of modern financial market development

This article deals with the functioning of the modern financial market in the context of increasing innovation trends and the transformation of knowledge into a full-fledged economic resource. The characteristics of knowledge as a resource are highlighted from the perspective of key participants in the financial market using dialectic and abstraction methods. It has been established that in the post-industrial economy, information and knowledge have become vital resources and radically changed the principles of economic relations. Owning information and knowledge and the ability to use them forms significant competitive advantages for all economic agents without exception. In turn, analysis and synthesis methods have been used to study the innovative components of the modern financial market. It has been determined that the rapid spread of financial innovations has a contradictory nature. On the one hand, new opportunities arise for participants in the financial market, but new threats and risks also emerge. These imbalances directly result from the information-knowledge asymmetry, which has significantly intensified under modern conditions. It is argued that the development of global information asymmetry has yet to weaken information asymmetry. The massive quantitative growth of information flows forms fundamentally new approaches to their use in the financial market, primarily based on digital technologies. The article argues that the innovative and knowledge trend of the modern financial market is of a long-term nature and dictates a rapid digital transformation. The spread of digital transformations, on the one hand, is precisely the result of the innovative and knowledge paradigm of financial market development, and on the other, digitization directly "fuels" innovative trends. The innovative and knowledge model of the modern financial market forms a fundamentally new agenda for the state as a regulator. Keywords: financial market, financial intermediaries, financial instruments, individual investors, financial literacy, innovations, knowledge.

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

AbstractWe introduce a new exotic option to be used within structured products to address a key disadvantage of standard time‐invariant portfolio protection: the well‐known cash‐lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option‐based structure with a dynamic allocation logic as underlying. We provide an in‐depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek‐type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time‐invariant portfolio protection strategies, meanwhile being also afraid to experience a cash‐lock event triggered by market turmoils.

Application of VMD–SSA–BiLSTM algorithm to smart grid financial market time series forecasting and sustainable innovation management

Introduction: This paper proposes a deep learning algorithm based on the VMD-SSA-BiLSTM model for time series forecasting in the smart grid financial market. The algorithm aims to extract useful information from power grid signals to improve the timing prediction accuracy and meet the needs of sustainable innovation management.Methods: The proposed algorithm employs the variational mode decomposition (VMD) method to decompose and reduce the dimensionality of historical data, followed by singular spectrum analysis (SSA) to perform singular spectrum analysis on each intrinsic mode function component. The resulting singular value spectrum matrices serve as input to a bidirectional long short-term memory (BiLSTM) neural network, which learns the feature representation and prediction model of the smart grid financial market through forward propagation and backpropagation.Results: The experimental results demonstrate that the proposed algorithm effectively predicts the smart grid financial market's time series, achieving high prediction accuracy and stability. The approach can contribute to sustainable innovation management and the development of the smart grid.Discussion: The VMD-SSA-BiLSTM algorithm's efficiency in extracting useful information from power grid signals and avoiding overfitting can improve the accuracy of timing predictions in the smart grid financial market. The algorithm's broad application prospects can promote sustainable innovation management and contribute to the development of the smart grid.

Reassessment of the role and functions of the Russian financial market in the context of structural transformation of the economy

A well-developed financial market has a central role in the savings management and investments in the economy and accelerates the economic growth. Geopolitical events in Ukraine, in which Russia got involved in February of 2022, fundamentally changed Russia’s foreign trade policy in terms of export-import payments. A large number of external and internal restrictions left a considerable impact on the effectiveness of the previous model of the Russian financial market. Today our country faces the need to carry out radical structural changes in its economy. Due to this fact there is an evident increase in the importance of the problems identification in the Russian financial market as well as in the development of optimal solutions of the issue. The purpose of this article is to assess the role and dynamics of the financial market’s development before and after the February events of 2022. Moreover, the article makes an emphasis on the change in the functions performance quality of the financial market.

No-arbitrage conditions and pricing from discrete-time to continuous-time strategies

In this paper, a general framework is developed for continuous-time financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then compare the usual no-arbitrage conditions of the literature, e.g. the usual no-arbitrage conditions NFL, NFLVR and NUPBR and the recent AIP condition. With appropriate pseudo-distance topologies, we show that they hold in continuous time if and only if they hold in discrete time. Moreover, the super-hedging prices in continuous time coincide with the discrete-time super-hedging prices, even without any no-arbitrage condition.

FINANCIAL MARKET AS A BASIS FOR EVALUATING TRANSFORMATION PROCESSES AND FORECASTING ITS EFFICIENCY THROUGH PERFORMANCE: CLASSIFICATION AND FORMS

The financial market model should be formed taking into account a clearly defined subject area and its objects, which is ensured by their classification and adequate representation in form. The described processes are significant since the type and forms of expression of the financial market form the basis for launching evaluation methods and forecasting its effectiveness through performance. The financial market classification consists of supplementing its model with the location and organization of its interrelated elements. It should be noted that for this purpose, systems for dividing objects into groups according to predetermined characteristics should be applied, in particular: 1) division of the financial market according to information about it (into groups, subgroups according to a particular characteristic); 2) allocation of logical connections between groups and subgroups of the financial market. These object distribution systems are based on the identification/construction of structures forming a combinatorial financial market model. The purpose of the article is the process of research the classification and forms of presentation of the financial market as a basis for evaluating transformational processes and forecasting their effectiveness through effectiveness. The process of researching the classification and forms of presentation of the financial market as a basis for evaluating transformational processes and forecasting its effectiveness through effectiveness is revealed. The main approaches to the classification of the financial market are characterized (by generalized, syncretic, and LOD approaches). The structuring of the financial need based on the convergence of economic relations with the transfer of ownership and the specifics of the legislative regulation of this process is essential and provides the presentation of information in terms of such components as currency market, deposit market, credit market; Securities Market; derivatives market; real estate market. The outlined approach to structuring the financial market forms a conceptual understanding of its model as a system S, which reflects the basic structures necessary to determine the objects of assessment and directions of performance forecasting through performance. To ensure the practical applicability of the conceptual model, modeling procedures, methods and algorithms must be systematically characterized.

Dynamic programming principle and computable prices in financial market models with transaction costs

How to compute (super) hedging costs in rather general financial market models with transaction costs in discrete-time? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it remains difficult to deduce numerical procedure to estimate them. We establish here a dynamic programming principle and we prove that it is possible to implement it under some conditions on the conditional supports of the price and volume processes for a large class of market models including convex costs such as order books but also non convex costs, e.g. fixed cost models.

Data-driven control of agent-based models: An Equation/Variable-free machine learning approach

We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modeled via microscopic/agent-based simulators. The approach obviates the need for construction of surrogate, reduced-order models. The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning, in particular, non-linear manifold learning (Diffusion Maps (DMs)) identifies a set of coarse-grained variables that parametrize the low-dimensional manifold on which the emergent/collective dynamics evolve. The out-of-sample extension and pre-image problems, i.e. the construction of non-linear mappings from the high-dimensional input space to the low-dimensional manifold and back, are solved by coupling DMs with the Nyström extension and Geometric Harmonics, respectively; (B) having identified the manifold and its coordinates, we exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics; then (C) based on the previous steps, we design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states, thus demonstrating that the scheme is robust against numerical approximation errors and modeling uncertainty. The efficiency of the framework is illustrated by controlling emergent unstable (i) traveling waves of a deterministic agent-based model of traffic dynamics, and (ii) equilibria of a stochastic financial market model with mimesis.