arXiv subjects

Ioane Muni Toke

Publications and source records attributed to Ioane Muni Toke.

At least 19 recordsLinked to original sources

arXiv2026

Optimal risk-aware interest rates for decentralized lending protocols

Interest rates in decentralized lending protocols are set algorithmically and adjust to supply and demand for liquidity. In this study, we propose an optimal interest rate model that maximizes the expected lender wealth while incorporating penalties for liquidity risk and interest rate stabilization. This objective benefits both sides of the market: it improves yield and reduces liquidity risk for lenders, while encouraging borrower activity indirectly through higher utilization and directly through stabilized borrowing costs. The dynamics of the utilization rate are modeled using point processes whose intensities depend on the interest rate. When intensities are linear, the optimal interest rate model is derived from a system of Riccati-type ODEs. In the nonlinear case, we approximate it using a Monte-Carlo estimator coupled with deep learning techniques. Finally, using block-by-block data, we conduct a risk-adjusted profit and loss analysis to compare industry-standard interest rate models to the deep learning-based one.

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arXiv2026

Optimal execution on Uniswap v2/v3 under transient price impact

We study the optimal liquidation of a large position on Uniswap v2 and Uniswap v3 in discrete time. The instantaneous price impact is derived from the AMM pricing rule. Transient impact is modeled to capture either exponential or approximately power-law decay, together with a permanent component. In the Uniswap v2 setting, we obtain optimal strategies in closed-form under general price dynamics. For Uniswap v3, we consider a two-layer liquidity framework, which naturally extends to multiple layers. We address the problem using dynamic programming under geometric Brownian motion dynamics and approximate the solution numerically using a discretization scheme. We obtain optimal strategies akin to classical ones in the LOB literature, with features specific to Uniswap. In particular, we show how the liquidity profile influences them.

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arXiv2025

Deep learning of point processes for modeling high-frequency data

We investigate applications of deep neural networks to a point process having an intensity with mixing covariates processes as input. Our generic model includes Cox-type models and marked point processes as well as multivariate point processes. An oracle inequality and a rate of convergence are derived for the prediction error. A simulation study shows that the marked point process can be superior to the simple multivariate model in prediction. We apply the marked ratio model to real limit order book data

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arXiv2025

High-Frequency Market Manipulation Detection with a Markov-modulated Hawkes process

This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We extend the model to general Hawkes excitation kernels that are piecewise constant between events. We develop an expectation-maximization algorithm for the statistical inference of the Hawkes intensities parameters as well as the state transition probabilities. The numerical convergence of the estimators is extensively tested on simulated data. Using high-frequency cryptocurrency data on a top centralized exchange, we apply the model to the detection of anomalous bursts of trades. We benchmark the goodness-of-fit of the model with the Markov-modulated Poisson process and demonstrate the relevance of the model in detecting suspicious activities.

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arXiv2024

Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets

We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral equation of the second kind. Using recent advances in solving partial differential equations with physics-informed neural networks, we provide a numerical procedure to solve this integral equation in high dimension. Together with an adapted training pipeline, we give a generic set of hyperparameters that produces robust results across a wide range of kernel shapes. We conduct an extensive numerical validation on simulated data. We finally propose two applications of the method to the analysis of the microstructure of cryptocurrency markets. In a first application we extract the influence of volume on the arrival rate of BTC-USD trades and in a second application we analyze the causality relationships and their directions amongst a universe of 15 cryptocurrency pairs in a centralized exchange.

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arXiv2024

Equity auction dynamics: latent liquidity models with activity acceleration

Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in turn, results in a reduced price impact and decreased volatility of the indicative price. In this study, we adapt the latent/revealed order book framework to the specifics of equity auctions. We provide precise measurements of the model parameters, including order submissions, cancellations, and diffusion rates. Our setup allows us to describe the full dynamics of the average order book during closing auctions in Euronext Paris. These findings support the relevance of the latent liquidity framework in describing limit order book dynamics. Lastly, we analyze the factors contributing to a sub-diffusive indicative price and demonstrate the absence of indicative price predictability.

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arXiv2023

Price impact in equity auctions: zero, then linear

Using high-quality data, we report several statistical regularities of equity auctions in the Paris stock exchange. First, the average order book density is linear around the auction price at the time of auction clearing and has a large peak at the auction price. While the peak is due to slow traders, the order density shape is the result of subtle dynamics. The impact of a new market order or cancellation at the auction time can be decomposed into three parts as a function of the size of the additional order: (1) zero impact, caused by the discrete nature of prices, sometimes up to a surprisingly large additional volume relative to the auction volume (2) linear impact for additional orders up to a large fraction of the auction volume (3) for even larger orders price impact is non-linear, frequently super-linear.

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arXiv2021

LOB modeling using Hawkes processes with a state-dependent factor

A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.

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arXiv2020

Marked point processes and intensity ratios for limit order book modeling

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent component specific to each mark within each process. We show that for specific mark distributions, this model is a combination of the ratio models defined in Muni Toke and Yoshida (2020). We prove convergence results for the quasi-maximum and quasi-Bayesian likelihood estimators of this model and provide numerical illustrations of the asymptotic variances. We use these ratio processes in order to model transactions occuring in a limit order book. Model flexibility allows us to investigate both state-dependency (emphasizing the role of imbalance and spread as significant signals) and clustering. Calibration, model selection and prediction results are reported for high-frequency trading data on multiple stocks traded on Euronext Paris. We show that the marked ratio model outperforms other intensity-based methods (such as "pure" Hawkes-based methods) in predicting the sign and aggressiveness of market orders on financial markets.

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arXiv2019

Analyzing order flows in limit order books with ratios of Cox-type intensities

We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters can be estimated by quasi likelihood maximization, without any interference from the baseline intensity. Consistency and asymptotic behavior of the estimators are given in several frameworks, and model selection is discussed with information criteria and penalization. The model is well-suited for high-frequency financial data: fitted models using easily interpretable covariates show an excellent agreement with empirical data. Extensive investigation on tick data consequently helps identifying trading signals and important factors determining the limit order book dynamics. We also illustrate the potential use of the framework for out-of-sample predictions.

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arXiv2017

Testing the causality of Hawkes processes with time reversal

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

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arXiv2016

Reconstruction of Order Flows using Aggregated Data

In this work we investigate tick-by-tick data provided by the TRTH database for several stocks on three different exchanges (Paris - Euronext, London and Frankfurt - Deutsche Börse) and on a 5-year span. We use a simple algorithm that helps the synchronization of the trades and quotes data sources, providing enhancements to the basic procedure that, depending on the time period and the exchange, are shown to be significant. We show that the analysis of the performance of this algorithm turns out to be a a forensic tool assessing the quality of the aggregated database: we are able to track through the data some significant technical changes that occurred on the studied exchanges. We also illustrate the fact that the choices made when reconstructing order flows have consequences on the quantitative models that are calibrated afterwards on such data. Our study also provides elements on the trade signature, and we are able to give a more refined look at the standard Lee-Ready procedure, giving new elements on the way optimal lags should be chosen when using this method. The findings are in line with both financial reasoning and the analysis of an illustrative Poisson model of the order flow.

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arXiv2016

Modelling intensities of order flows in a limit order book

We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders and cancellations. For cancellations, we introduce the concept of "priority index" to describe the selection of orders to be cancelled in the order book. Parameters of the model are estimated using likelihood maximization. We illustrate the performance of the model by providing extensive simulation results, with a comparison to empirical data and a standard Poisson reference.

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arXiv2015

Stationary distribution of the volume at the best quote in a Poisson order book model

In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.

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arXiv2014

Exact and asymptotic solutions of the call auction problem

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.

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arXiv2013

The order book as a queueing system: average depth and influence of the size of limit orders

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 results for birth-and-death processes, we build an analytical formula for the shape (depth) of a continuous order book model which is both founded by market mechanisms and very close to empirically tested formulas. We relate this shape to the probability of execution of a limit order, highlighting a law of conservation of the flows of orders in an order book. We then extend our model by allowing random sizes of limit orders, hereby allowing to study the relationship between the size of the incoming limit orders and the shape of the order book. Our theoretical model shows that, for a given total volume of incoming limit orders, the less limit orders are submitted (i.e. the larger the average size of these limit orders), the deeper is the order book around the spread. This theoretical relationship is finally empirically tested on several stocks traded on the Paris stock exchange.

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arXiv2010

Econophysics: Empirical facts and agent-based models

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words Economics and Physics, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modelling), econometrics of financial bubbles and crashes, etc. In the first part of the review, we discuss on the emergence of Econophysics. Then we present empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged stylized facts which describe the returns of financial assets- fat tails, volatility clustering, autocorrelation, etc.- and recall that some of these properties are directly linked to the way time is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. In the second part of the review, we deal with models in Econophysics through the point of view of agent-based modelling. Amongst a large number of multi-agent-based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that are extensively presented here. Second, kinetic theory models designed to explain some empirical facts on wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.

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arXiv2010

"Market making" behaviour in an order book model and its impact on the bid-ask spread

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.

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