Empirical properties of asset returns: stylized facts and statistical issues

Rama Cont, 2001

📕 Paper

He shares findings from a statistical analysis of price changes in different financial markets. He talks about general issues in studying financial data and describes various properties of asset returns, such as distribution, tail properties, extreme changes, and dependencies. He highlights common features across different markets and instruments. Finally, he explains how these properties challenge traditional statistical methods used in financial data analysis and discusses the issues faced in each situation.

A Stochastic Model for Order Book

Rama Cont, Sasha Stoikov, Rishi Talreja, 2010

📕 Paper

They suggest a continuous-time model for limit order book dynamics that is easy to estimate from data, captures key empirical properties, and allows for quick calculations without simulation. They explain a parameter estimation method using high-frequency order book data and demonstrate it with Tokyo Stock Exchange data. By using matrix calculations and Laplace transform methods, they efficiently compute event probabilities based on the order book's state. They show that their model effectively captures short-term limit order book dynamics using high-frequency data and assess a simple trading strategy based on their findings.

Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations

Rama Cont, Adrien de Larrard, 2012

📕 Paper

They suggest a model to study how buy and sell orders change quickly in a busy market. They find a way to simplify the model using a process called Markovian jump-diffusion. This makes it easier to predict things like price changes and how long it takes for the next price move. Their method works for many different assumptions and models, including ones based on Poisson point processes, self-exciting point processes, and ACD-GARCH models.

Optimal Execution of Portfolio Transactions

Robert Almgren, Neil Chriss, 2000

📕 Paper

They study how to carry out portfolio transactions while reducing both price changes and transaction costs. Using a basic cost model, they create a range of strategies that balance these factors over time. They can choose the best approach by minimizing a certain value or by considering the tradeoff between price change risk and transaction costs, which they call Liquidity-adjusted Value at Risk (L-VaR).

Bayesian Adaptive Trading with a Daily Cycle

Robert Almgren, Julian Lorenz, 2006

📕 Paper

In this study, they create a model that accounts for the daily cycle in algorithmic trading. The trader uses price information throughout the day to update their estimates of other traders' targets and directions. This helps determine an optimal trade schedule to minimize trading costs while following sign constraints. Although the strategies are based on simple dynamic reasoning, they are actually the globally optimal strategies that dynamic programming would determine.

The Mathematics of Optimal Execution

Olivier Guéant, 2016

📕 Paper

This paper present the mathematical models most commonly used to solve optimal execution problems in finance. It presents a general modeling framework for optimal execution problems–inspired from the Almgren-Chriss approach–and then demonstrates the use of that framework across a wide range of areas.

How markets slowly digest changes in supply and demand

Jean-Philippe Bouchaud, J. Doyne Farmer, Fabrizio Lillo, 2008

📕 Paper

In this article, they reexamine price formation in market microstructure, focusing on how supply and demand fluctuations are incorporated into prices. Large orders take a long time to trade due to low market liquidity, resulting in highly persistent order flow. This affects price formation, liquidity dynamics, and market impact. They review theories that make quantitative predictions about market impact, bid-ask spread, order book dynamics, and volatility, finding encouraging successes when compared to data. This framework suggests that most information comes from supply and demand rather than external news, which is relevant for market regulation, agent-based models, execution strategies, and market ecologies.

No-Dynamic-Arbitrage and Market Impact

Jim Gatheral, 2008

📕 Paper

In this study, they establish a connection between the market impact function, which shows how market price responds to traded quantity, and the decay of market impact. They demonstrate that exponential decay of market impact is only compatible with linear market impact. They also derive various inequalities linking the typical shape of the market impact function to the decay of market impact and observe that these inequalities are usually close to being equalities in practice.

High-frequency trading in a limit order book

Marco Avellaneda, Sasha Stoikov, 2008

📕 Paper

They investigate how a stock dealer can decide on bid and ask quotes in a limit order book. The dealer faces risks due to price changes and the random arrival of buy and sell orders. They use a two-step process to solve this problem: first, the dealer calculates a personal value for the stock based on their inventory; then, they adjust their bid and ask quotes according to the market. They compare this "inventory-based" strategy to a simpler one and find that their approach results in less variation in profits and final inventories.

Dealing with the Inventory Risk. A solution to the market making problem

Olivier Guéant, Charles-Albert Lehalle, Joaquin Fernandez Tapia, 2011

📕 Paper

Market makers need to set bid and ask quotes for stocks while balancing their potential returns and the price risk from their inventory. In this study, they look at a similar problem to the one studied by Ho and Stoll, and Avellaneda and Stoikov. They use a model where the market has a reference price that changes randomly, and the arrival rates of buy and sell orders depend on this reference price. The market maker aims to maximize their profit within a specific time frame. They show that the equations for this problem can be simplified and solved when considering inventory limits. They also examine the behavior of the optimal quotes and suggest approximations based on a special analysis of these quotes.