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In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and…

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…

We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show…

Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential…

We propose a new model for the level I of a Limit Order Book (LOB), which incorporates the information about the standing orders at the opposite side of the book after each price change and the arrivals of new orders within the spread. Our…

We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…

This research presents a comprehensive framework for analyzing liquidity in financial markets, particularly in the context of high-frequency trading. By leveraging advanced machine learning classification techniques, including Logistic…

One of the most fundamental questions in quantitative finance is the existence of continuous-time diffusion models that fit market prices of a given set of options. Traditionally, one employs a mix of intuition, theoretical and empirical…

In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this article we consider a limit order book model that allows for time-dependent, deterministic depth and resilience of the book and…

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…

In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we…

We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers…

We postulates, and then show experimentally, that liquidity deficit is the driving force of the markets. In the first part of the paper a kinematic of liquidity deficit is developed. The calculus-like approach, which is based on…

We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair…

We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…

In this paper, we describe a novel agent-based approach for modelling the transaction cost of buying or selling an asset in financial markets, e.g., to liquidate a large position as a result of a margin call to meet financial obligations.…

This study explores the prediction of high-frequency price changes using deep learning models. Although state-of-the-art methods perform well, their complexity impedes the understanding of successful predictions. We found that an…

Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with both static and dynamic components. They…

In this research, we have empirically investigated the key drivers affecting liquidity in equity markets. We illustrated how theoretical models, such as Kyle's model, of agents' interplay in the financial markets, are aligned with the…

This paper studies the fill probabilities of limit orders placed at different price levels in a limit order book. These probabilities play a central role in execution optimization, as limit orders are not guaranteed to be executed and…