Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
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48 results for “market shaping”
In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on and convex on for some . We study the corresponding Hamilton-Jacobi-…
In this short note, we study an optimization problem of expected implementation shortfall (IS) cost under general shaped market impact functions. In particular, we find that an optimal strategy is a VWAP (volume weighted average price) execution strategy when the market model is a Black-Scholes type with stochastic clo…
Performative Market Makingq-fin.TR
Financial models shape markets through performativity, creating self-fulfilling prophecies.
problem Lack of mathematical formulation for performativity in financial markets.
method Embedding the model in the market process, creating a closed feedback loop.
result Performative market makers can reverse engineer dominant strategies and arbitrage them.
The paper explores risk measures and arbitrage in financial markets.
problem Quantifying and managing risk in financial markets.
method Introduces new risk measure axioms and characterizes arbitrage conditions.
result Derives the consistent price interval for financial contracts.
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a n…
W-shaped vol curves in liquid options can be modeled with two variance-gamma models.
problem Reproducing W-shaped implied volatility curves in liquid option markets.
method Using a mixture of two variance-gamma models.
result W-shaped vol curves can be generated with fewer distributions (two) compared to lognormal models (at least three).
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product d…
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) stock components are arranged in ascending order from the smallest one in…
This study proves new financial market theorems breaking standard risk definitions.
problem Breaking standard risk definitions in financial markets.
method Presenting proofs for new financial market theorems.
result New definitions are richer and broader than standard ones considering shape.
New game theory approach to bond market liquidity and participant behavior.
problem Uncertainty in market maker types and regulatory structure.
method Liquidity Game theory applied to UK bond market interactions.
result Strategies and structures for market makers and regulators.
The paper models intraday power prices using fundamental drivers.
problem Lack of research on drivers for intraday price processes.
method Modelling location, shape, and scale of intraday price distribution using fundamental variables.
result Significant improvements in probabilistic forecasting performance, especially in tails.
Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the bivariate probability distribution P(x,y) [1,2,3,4]. There are two properties, the…
We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that…
How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price impact has a universal non-linear shape for trades aggregated on any intra-day sc…
Limit Order Book (LOB) shape modeling in presence of heterogeneously informed market participantsq-fin.TR
Paper models limit order book with informed traders and market makers.
problem Modeling the limit order book with heterogeneous market participants.
method Agent-based model with four types of participants: informed traders, noise traders, informed market makers, and noise market makers. Based on Glosten-Milgrom and Huang-Rosenbaum-Saliba approaches.
result Derived the static limit order book characteristics and compared them with existing models.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
problem Understanding price dynamics and bubbles in multi-asset markets.
method Derives sufficient and necessary conditions for average equilibrium price dynamics in a two-asset model.
result Assets with positive average dividends display hump-shaped bubbles, while those with constant fundamental values show misvaluation effects.
A Cultural Market Modelq-fin.GN
Social interactions and personal tastes shape our consumption behavior of cultural products. In this study, we present a computational model of a cultural market and we aim to analyze the behavior of the consumer population as an emergent phenomena. Our results suggest that the final market shares of cultural products …
We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter . We also prove the convergence of the discrete-time process describing the…
In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the lev…
Unified theory explains market impact using a simplified supply-demand parameter.
problem Understanding the market impact of metaorders and excess volatility.
method Coarse-grained approach with a single parameter ρ to model supply-demand equilibrium and market impact.
result Establishes a connection between excess volatility and order-driven markets through the square-root law.
We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell LOBs. Th…
Study optimal stock purchases under fluctuating market resilience.
problem Optimal stock purchases over time with varying market resilience.
method Model market resilience and liquidity variations, solve optimization problem.
result Unique optimal execution strategy found.
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
In this article we discuss the distribution of asset price movements by the market potential function. From the principle of free energy minimization we analyze two different kinds of market potentials. We obtain a U-shaped potential when market reversion (i.e. contrarian investors) is dominant. On the other hand, if t…
Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a sing…
Exchange uses incentives to optimize limit order book dynamics.
problem Optimizing market liquidity in fragmented electronic markets.
method Modeling limit order book as SPDE and using control theory to design incentives.
result Exchange can design incentives to modify order book shape and increase liquidity.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable to quantify investor sentiment and simulate U- and Swoosh-shaped recovery.
result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.
This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is prop…
This paper investigates the market impact of passive orders.
problem Understanding the market impact of passive orders executed through limit orders.
method Developed a microstructure model linking liquidity dynamics and price moves, replacing the constant information content assumption with a function dependent on available volume.
result Derived useful approximations for market impact curves, leading to closed-form formulas.
For a commodity spot price dynamics given by an Ornstein-Uhlenbeck process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium i…
New MMM captures hierarchical marketing effects and sign restrictions.
problem Measuring effectiveness of marketing activities with hierarchical structure and sign constraints.
method Proposes a constrained maximum likelihood approach using Hamiltonian Monte Carlo algorithm.
result Demonstrates superior performance on real datasets compared to multi-stage methods.
Continuous-time model shows insider trading constraints impact market dynamics.
problem Trading constraints faced by insiders in continuous-time models.
method Proved global existence of equilibrium with terminal trading constraint.
result Equilibrium model aligns with empirical market behaviors.
Kriging predicts futures prices by accounting for trends and bid-ask spreads.
problem Predicting futures prices with trends and bid-ask spreads.
method Bayesian Kriging technique to model term structure.
result Kriging accurately predicts futures prices with embedded trends and bid-ask spreads.
This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust index of the dynamics of the market structure and provides information on the int…
In this paper, we studied the dynamics of the log-return distribution of the Korean Composition Stock Price Index (KOSPI) from 1992 to 2004. Based on the microscopic spin model, we found that while the index during the late 1990s showed a power-law distribution, the distribution in the early 2000s was exponential. This…
The order book as a queueing system: average depth and influence of the size of limit ordersq-fin.TR
We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic result…
Market Ecology, Pareto Wealth Distribution and Leptokurtic Returns in Microscopic Simulation of the LLS Stock Market Modelcond-mat.stat-mech
The LLS stock market model is a model of heterogeneous quasi-rational investors operating in a complex environment about which they have incomplete information. We review the main features of this model and several of its extensions. We study the effects of investor heterogeneity and show that predation, competition, o…
Machine Learning for Yield Curve Feature Extraction: Application to Illiquid Corporate Bondsq-fin.ST
This paper studies an application of machine learning in extracting features from the historical market implied corporate bond yields. We consider an example of a hypothetical illiquid fixed income market. After choosing a surrogate liquid market, we apply the Denoising Autoencoder (DAE) algorithm to learn the features…
Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…
Understanding how funding and 4H context regulate crypto markets.
problem Analyzing the chaotic appearance of financial markets.
method Observing interactions between market context and capital conditions in the 4H timeframe.
result Ranges in crypto markets are strategic positioning by informed participants, not indecision.
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion…
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…
Unified model explains volatility memory in stocks and forex.
problem Understanding the components of volatility memory in financial markets.
method Developed a three-dimensional decomposition of volatility memory into level, shape, and tempo.
result Unified model shows that volatility memory is state-dependent, with different gates prevailing in equities and forex.
Study shows informed traders harm market makers but price discovery benefits outweigh costs.
problem Informed traders' impact on market makers' profitability.
method Agent-based model with heterogeneous learning agents, multi-agent reinforcement learning.
result Informed market order flow is harmful when aggregate informedness is low but beneficial as it increases.
K-expectiles clusteringstat.ME
Proposes a new clustering method based on expectiles for non-spherical clusters.
problem Inability of -means to handle non-spherical clusters.
method Uses expectiles to define cluster centers and searches for clusters via a greedy algorithm.
result Outperforms -means and spectral clustering on asymmetric shaped clusters.
This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistrib…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semim…