scholarly journals Optimal inventory management and order book modeling

2019 ◽  
Vol 65 ◽  
pp. 145-181 ◽  
Author(s):  
Nicolas Baradel ◽  
Bruno Bouchard ◽  
David Evangelista ◽  
Othmane Mounjid
Keyword(s):  
Inventory Management ◽  
High Frequency ◽  
Limit Order Book ◽  
Order Book ◽  
Value Functions ◽  
Limit Order ◽  
Terminal Wealth ◽  
Market Makers ◽  
Market Participants ◽  
The One

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [12, 18, 19], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

High Frequency Asymptotics for the Limit Order Book

2016 ◽  
Vol 02 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Peter Lakner ◽  
Josh Reed ◽  
Sasha Stoikov
Keyword(s):  
Poisson Process ◽  
High Frequency ◽  
Limit Order Book ◽  
Order Book ◽  
Limit Order ◽  
Limit Orders ◽  
Long Run ◽  
Frequency Regime ◽  
Market Orders ◽  
The One

We study the one-sided limit order book corresponding to limit sell orders and model it as a measure-valued process. Limit orders arrive to the book according to a Poisson process and are placed on the book according to a distribution which varies depending on the current best price. Market orders to buy periodically arrive to the book according to a second, independent Poisson process and remove from the book the order corresponding to the current best price. We consider the above described limit order book in a high frequency regime in which the rate of incoming limit and market orders is large and traders place their limit sell orders close to the current best price. Our first set of results provide weak limits for the unscaled price process and the properly scaled measure-valued limit order book process in the high frequency regime. In particular, we characterize the limiting measure-valued limit order book process as the solution to a measure-valued stochastic differential equation. We then provide an analysis of both the transient and long-run behavior of the limiting limit order book process.

scholarly journals The Relation between Intraday Limit Order Book Depth and Spread

2021 ◽  
Vol 9 (4) ◽  
pp. 60
Author(s):  
Alexandre Aidov ◽  
Olesya Lobanova
Keyword(s):  
Generalized Method Of Moments ◽  
Limit Order Book ◽  
Order Book ◽  
Inverse Relation ◽  
Limit Order ◽  
Market Participants ◽  
Market Depth ◽  
Bid Ask Spread ◽  
Explanatory Factors ◽  
Trading Decisions

Prior studies that examine the relation between market depth and bid–ask spread are often limited to the first level of the limit order book. However, the full limit order book provides important information beyond the first level about the depth and spread, which affects the trading decisions of market participants. This paper examines the intraday behavior of depth and spread in the five-deep limit order book and the relation between depth and spread in a futures market setting. A dummy-variables regression framework is employed and is estimated using the generalized method of moments (GMM). Results indicate an inverse U-shaped pattern for depth and an increasing pattern for spread. After controlling for known explanatory factors, an inverse relation between the limit order book depth and spread is documented. The inverse relation holds for depth and spread at individual levels in the limit order book as well. Results indicate that market participants actively manage both the price (spread) and quantity (depth) dimensions of liquidity along the five-deep limit order book.

scholarly journals Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations

2021 ◽  
Author(s):  
Helder Rojas ◽  
Anatoly Yambartsev ◽  
Artem Logachov
Keyword(s):  
Large Deviations ◽  
Stochastic Models ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Limit Order Book ◽  
Order Book ◽  
Limit Order ◽  
Bid Ask Spread ◽  
Large Numbers ◽  
The One

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Patience vs. impatience of traders: Formation of the value-at-price distribution through competition for liquidity

2015 ◽  
Vol 02 (03) ◽  
pp. 1550029
Author(s):  
Peter Lerner
Keyword(s):  
Asymptotic Distribution ◽  
High Frequency ◽  
Imperfect Information ◽  
Limit Order Book ◽  
Order Book ◽  
Short Term ◽  
Limit Order ◽  
Price Distribution ◽  
Realistic Representation ◽  
Dynamic Version

The ability to postpone one's execution in the market without penalty in search of a better price is an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution price from market expectations and quotes. Equilibrium theory was provided in 2005 by Foucault, Kadan and Kandel. I derive an asymptotic distribution of the bids/offers as a function of the ratio of patient and impatient traders using the dynamic version of the Foucault, Kadan and Kandel limit order book (LOB) model. Our version of the LOB model allows stylized, but sufficiently realistic representation of the trading markets. In particular, dynamic LOB allows simulation of the distribution of execution times and spreads from high-frequency quotes. Significant analytic progress is made toward framing of short-term trading as competition for immediacy of execution between traders under imperfect information. The results are qualitatively compared with empirical volume-at-price distribution of highly liquid stocks.

scholarly journals Volatility and Depth in Commodity and FX Futures Markets

2021 ◽  
Vol 14 (11) ◽  
pp. 545
Author(s):  
Alexandre Aidov ◽  
Olesya Lobanova
Keyword(s):  
Method Of Moments ◽  
Futures Markets ◽  
Generalized Method Of Moments ◽  
Limit Order Book ◽  
Order Book ◽  
Positive Relation ◽  
Limit Order ◽  
Market Participants ◽  
Market Depth ◽  
Foreign Exchange Futures

Prior theory suggests a positive relation between volatility and market depth, while past empirical research finds contrasting results. This paper examines the relation between the volatility and the limit order book depth in commodity and foreign exchange futures markets during a turbulent time using the generalized method of moments (GMM). Results indicate a negative relation between volatility and depth and suggest that the depth in the limit order book decreases as volatility increases. Findings help to understand how market participants provide liquidity in response to shifts in prices.

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