We present a mathematical study of the order book as a multidimensional continuous- time Markov chain where the order flow is modeled by independent Poisson processes. Our aim is to bridge the gap between the microscopic description of price formation (agent- based modeling), and the Stochastic...

This paper is devoted to the study of derivative hedging in incomplete markets when frictions are considered. We extend the general local risk minimisation approach introduced in [1] to account for liquidity costs, and derive the corresponding optimal strategies in both the discrete- and...

A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that liquidity balance on best bid/best ask is quite informative...

We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional...

This paper studies the question of filtering and maximizing terminal wealth from expected utility in a stochastic volatility models. The special feature is that the only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot...

Lead/lag relationships are an important stylized fact at high frequency. Some assets follow the path of others with a small time lag. We provide indicators to measure this phenomenon using tick-by-tick data. Strongly asymmetric cross-correlation functions are empirically observed, especially in...

Order splitting is a standard practice in trading : traders constantly scan the limit order book and choose to limit the size of their market orders to the quantity available at the best limit, thereby controlling the market impact of their orders. In this article, we focus on the other trades,...

In this paper, we establish a model for market making in options whose underlying is perfectly liquid. In our model framework, the stock price follows a generic stochastic volatility model under the real-world probability measure P. Market participants price options on this stock under a...

Using a new high frequency quality data set we provide a precise empirical study of the interdealer spot market. We check that the main stylized facts of financial time series are valid for the FX market: fat-tailed distribution of returns, aggregational normality and volatility clustering. We...

The aim of this study is to quantify the low latency advantage of High Frequency Trading (HFT) and to compute, empirically, an optimal holding period of a HF trader. Critics claim that low latency leads to information asymmetry victimizing retail investors. However, objective studies measuring...