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At least 217 records · Page 12Linked to original sources
arXiv2015

Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis

This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The natural framework we use is mean field game theory, a class of stochastic differential games with a continuum of anonymous players. Several sources of heterogeneity are considered including the mean size of orders. Thus we are able to consider the coexistence of Institutional Investors and High Frequency Traders (HFT). We provide both analytical solutions and numerical experiments. Implications on classical quantities are explored: order book size, prices, and effective bid/ask spread. According to the model, in markets with Institutional Investors only we show the existence of inefficient liquidity imbalances in equilibrium, with two symmetrical situations corresponding to what we call liquidity calls for liquidity. During these situations the transaction price significantly moves away from the fair price. However this macro phenomenon disappears in markets with both Institutional Investors and HFT, although a more precise study shows that the benefits of the new situation go to HFT only, leaving Institutional Investors even with higher trading costs.

q-fin.TR↗
arXiv2013

BSDEs with singular terminal condition and control problems with constraints

We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [7] and [8]. We perform a verification and discuss special cases for which the control problem has explicit solutions.

math.OC↗
arXiv2016

Continuous-Time Random Walk with multi-step memory: An application to market dynamics

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.

physics.data-an↗
arXiv2013

A theoretical framework for trading experiments

A general framework is suggested to describe human decision making in a certain class of experiments performed in a trading laboratory. We are in particular interested in discerning between two different moods, or states of the investors, corresponding to investors using fundamental investment strategies, technical analysis investment strategies respectively. Our framework accounts for two opposite situations already encountered in experimental setups: i) the rational expectations case, and ii) the case of pure speculation. We consider new experimental conditions which allow both elements to be present in the decision making process of the traders, thereby creating a dilemma in terms of investment strategy. Our theoretical framework allows us to predict the outcome of this type of trading experiments, depending on such variables as the number of people trading, the liquidity of the market, the amount of information used in technical analysis strategies, as well as the dividends attributed to an asset. We find that it is possible to give a qualitative prediction of trading behavior depending on a ratio that quantifies the fluctuations in the model.

q-fin.TR↗
arXiv2014

VWAP execution and guaranteed VWAP

Optimal liquidation using VWAP strategies has been considered in the literature, though never in the presence of permanent market impact and only rarely with execution costs. Moreover, only VWAP strategies have been studied and the pricing of guaranteed VWAP contracts has never been addressed. In this article, we develop a model to price guaranteed VWAP contracts in a general framework for market impact and we highlight the differences between an agency VWAP and a guaranteed VWAP contract. Numerical methods and applications are also provided.

q-fin.TR↗
arXiv2014

Random Market Models with an H-Theorem

In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential wealth distribution as asymptotic equilibrium, independently of the effectiveness of the transactions and of the limitation of the total wealth. The entropy increases with time in these models and the existence of an H-theorem is computationally checked. Also, it is shown that any small perturbation of the models equations make them to lose the exponential distribution as an equilibrium solution.

q-fin.TR↗
arXiv2013

Modeling of Stock Returns and Trading Volume

In this study, we investigate the statistical properties of the returns and the trading volume. We show a typical example of power-law distributions of the return and of the trading volume. Next, we propose an interacting agent model of stock markets inspired from statistical mechanics [24] to explore the empirical findings. We show that as the interaction among the interacting traders strengthens both the returns and the trading volume present power-law behavior.

q-fin.ST↗
arXiv2013

Grand canonical minority game as a sign predictor

In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously degenerated system, when only one agent is involved. The prediction is the most efficient if the agent is equipped with all strategies from the Full Strategy Space. Each of these filters is evaluated and, in each step, the best one is chosen. Despite the casual simplicity of the method its usefulness is invaluable in many cases including real problems. The significant power of the method lies in its ability to fast adaptation if λ-GCMG modification is used. The success rate of prediction is sensitive to the properly set memory length. We considered the feasibility of prediction for the Minority and Majority games. These two games are driven by different dynamics when self-generated time series are considered. Both dynamics tend to be the same when a feedback effect is removed and an exogenous signal is applied.

stat.AP↗
arXiv2013

Futures market efficiency diagnostics via temporal two-point correlations. Russian market case study

Using a two-point correlation technique, we study emergence of market efficiency in the emergent Russian futures market by focusing on lagged correlations. The correlation strength of leader-follower effects in the lagged inter-market correlations on the hourly time frame is seen to be significant initially (2009-2011) but gradually goes down, as the erstwhile leader instruments -- crude oil, the USD/RUB exchange rate, and the Russian stock market index -- seem to lose the leader status. An inefficiency index, based on two-point correlations, is proposed and its history is established.

q-fin.TR↗
arXiv2013

Characterizing financial crisis by means of the three states random field Ising model

We propose a formula of time-series prediction by means of three states random field Ising model (RFIM). At the economic crisis due to disasters or international disputes, the stock price suddenly drops. The macroscopic phenomena should be explained from the corresponding microscopic view point because there are existing a huge number of active traders behind the crushes. Hence, here we attempt to model the artificial financial market in which each trader $i$ can choose his/her decision among `buying', `selling' or `staying (taking a wait-and-see attitude)', each of which corresponds to a realization of the three state Ising spin, namely, $S_{i}=+1$, -1 and $S_{i}=0$, respectively. The decision making of traders is given by the Gibbs-Boltzmann distribution with the energy function. The energy function contains three distinct terms, namely, the ferromagnetic two-body interaction term (endogenous information), random field term as external information (exogenous news), and chemical potential term which controls the number of traders who are watching the market calmly at the instance. We specify the details of the model system from the past financial market data to determine the conjugate hyper-parameters and draw each parameter flow as a function of time-step. Especially we will examine to what extent one can characterize the crisis by means of a brand-new order parameter --- `turnover' --- which is defined as the number of active traders who post their decisions $S_{i}=1,-1$, instead of $S_{i}=0$.

q-fin.TR↗
arXiv2013

A Pre-Trade Algorithmic Trading Model under Given Volume Measures and Generic Price Dynamics (GVM-GPD)

We make several improvements to the mean-variance framework for optimal pre-trade algorithmic execution, by working with volume measures and generic price dynamics. Volume measures are the continuum analogies for discrete volume profiles commonly implemented in the execution industry. Execution then becomes an absolutely continuous measure over such a measure space, and its Radon-Nikodym derivative is commonly known as the Participation of Volume (PoV) function. The four impact cost components are all consistently built upon the PoV function. Some novel efforts are made for these linear impact models by having market signals more properly expressed. For the opportunistic cost, we are able to go beyond the conventional Brownian-type motions. By working directly with the auto-covariances of the price dynamics, we remove the Markovian restriction associated with Brownians and thus allow potential memory effects in the price dynamics. In combination, the final execution model becomes a constrained quadratic programming problem in infinite-dimensional Hilbert spaces. Important linear constraints such as participation capping are all permissible. Uniqueness and existence of optimal solutions are established via the theory of positive compact operators in Hilbert spaces. Several typical numerical examples explain both the behavior and versatility of the model.

q-fin.TR↗
arXiv2015

Optimal Liquidity Provision

A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as for arbitrary preferences of the liquidity provider under consideration.

q-fin.TR↗
arXiv2013

Corporations and Regulators: The Game of Influence in Regulatory Capture

In a market system, regulations are designed to prevent or rectify market failures that inhibit fair exchange, such as monopoly or transactions with hidden costs. Because regulations reduce profits to those possessing unfair advantage, these advantaged corporations (whether individuals, companies, or other collective organizations) are motivated to influence regulators. Regulatory bodies created to protect the market are instead co-opted to advance the interests of the corporations they are charged to regulate. This wide-spread influence, known as "regulatory capture," has been recognized for over 100 years, and according to expectations of rational behavior, will exist wherever it is in the mutual self-interest of corporations and regulators. Here we model the interaction between corporations and regulators using a new game theory framework explicitly accounting for players' mutual influence, and demonstrate the incentive for collusion. Communication between corporations and regulators enables them to collude and split the resulting profits. We identify when collusion is profitable for both parties. The intuitive results show that capture occurs when the benefits to the corporation outweigh the costs to the regulator. Under these conditions, the corporation can compensate the regulator for costs incurred and, further, provide a profit to both parties. In the real world, benefits often far outweigh costs, providing large incentives to collude and making capture likely. Regulatory capture is inhibited by decreasing the influence between parties through strict separation, independent market knowledge and research by regulators, regulatory and market transparency, regulatory accountability for market failures, widely distributed regulatory control, and anti-corruption enforcement.

q-fin.GN↗
arXiv2013

Agent-Based Stock Market Model with Endogenous Agents' Impact

The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three fundamental stylised facts: fat-tail log returns, power-law volatility autocorrelation decay in time and volatility clustering.

q-fin.TR↗
arXiv2013

Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books

We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in the asymptotic regime supported by empirical observations the mid price and bid-ask-spread can be described using only certain parameters of the book (not the whole book itself). Our limit process is characterized by reflecting behavior and state-dependent jumps. Our analysis allows to explain certain characteristics observed in practice such as: the connection between power-law decaying tails in the volumes of the order book and the returns, as well as statistical properties of the long-run spread distribution.

q-fin.TR↗
arXiv2013

Random Matrix Application to Correlations Among Volatility of Assets

In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribution of a significant number of eigenvalues of the volatility correlation matrix matches with the analytical result from the RMT. Furthermore, the empirical estimates of short and long-range correlations among eigenvalues, which are within the RMT bounds, match with the analytical results for Gaussian Orthogonal ensemble (GOE) of the RMT. To understand the information content of the largest eigenvectors, we estimate the contribution of GICS industry groups in each eigenvector. In comparison with eigenvectors of correlation matrix for price fluctuations, only few of the largest eigenvectors of volatility correlation matrix are dominated by a single industry group. We also study correlations among `volatility return' and get similar results.

q-fin.ST↗
arXiv2015

High frequency trading and asymptotics for small risk aversion in a Markov renewal model

We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price itself. In this framework, we can reproduce the adverse selection risk, appearing in two different forms: the usual one due to big market orders impacting the stock price and penalizing the agent, and the weak one due to small market orders and reducing the probability of a profitable execution. We solve the market making problem by stochastic control techniques in this semi-Markov model. In the no risk-aversion case, we provide explicit formula for the optimal controls and characterize the value function as a simple linear PDE. In the general case, we derive the optimal controls and the value function in terms of the previous result, and illustrate how the risk aversion influences the trader strategy and her expected gain. Finally, by using a perturbation method, approximate optimal controls for small risk aversions are explicitly computed in terms of two simple PDE's, reducing drastically the computational cost and enlightening the financial interpretation of the results.

q-fin.TR↗