CROUHY Michel

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This thesis addresses various issues related to collateral management in the context of centralized trading through clearing houses. First, we present the notions of capital cost and funding cost for a bank, by placing them in an elementary Black-Scholes framework where the payoff of a standard call takes the place of a counterparty default exposure. We assume that the bank only imperfectly hedges this call and faces a funding cost higher than the risk-free rate, hence the FVA and KVA pricing corrections with respect to the Black-Scholes price. We then focus on the costs that a bank faces when trading in a CCP. To this end, we transpose the XVA framework of bilateral trading to centralized trading. The total cost for a member to trade through a CCP is thus decomposed into a CVA corresponding to the cost for the member to replenish its contribution to the guarantee fund in case of losses due to defaults by other members, an MVA corresponding to the cost of financing its initial margin and a KVA corresponding to the cost of capital put at risk by the member in the form of its contribution to the guarantee fund. We then question the regulatory assumptions previously used, looking at alternatives in which members would use a third party for their initial margin, who would post the margin in the member's place in exchange for a fee. We also consider a method of calculating the guarantee fund and its allocation that takes into account the risk of the chamber in the sense of the fluctuations of its P&L over the following year, as it results from the combination of the market risk and the default risk of the members. Finally, we propose the application of multivariate risk measure methodologies for the calculation of members' margins and/or guarantee funds. We introduce a notion of systemic risk measures in the sense that they are sensitive not only to the marginal risks of the components of a financial system (e.g., but not necessarily the positions of the members of a CCP), but also to their dependence.

In this thesis, we consider two types of applications of feedback effects in finance. These effects come into play when market participants execute sequences of trades or take part in chain reactions, which generate peaks of activity. The first part presents a dynamic optimal execution model in the presence of an exogenous stochastic market order flow. We start from the benchmark model of Obizheva and Wang, which defines an optimal execution framework with a mixed price impact. We add an order flow modeled using Hawkes processes, which are jump processes with a self-excitation property. Using stochastic control theory, we determine the optimal strategy analytically. Then we determine the conditions for the existence of Price Manipulation Strategies, as introduced by Huberman and Stanzl. These strategies can be excluded if the self-excitation of the order flow exactly offsets the price resilience. In a second step, we propose a calibration method for the model, which we apply on high frequency financial data from CAC40 stock prices. On these data, we find that the model explains a non-negligible part of the price variance. An evaluation of the optimal strategy in backtesting shows that it is profitable on average, but that realistic transaction costs are sufficient to prevent price manipulation. Then, in the second part of the thesis, we focus on the modeling of intraday volatility. In the literature, most of the backward-looking volatility models focus on the daily time scale, i.e., on day-to-day price changes. The objective here is to extend this type of approach to shorter time scales. We first present an ARCH-type model with the particularity of taking into account separately the contributions of past intraday and night-time returns. A calibration method for this model is studied, as well as a qualitative interpretation of the results on US and European stock returns. In the next chapter, we further reduce the time scale considered. We study a high-frequency volatility model, the idea of which is to generalize the Hawkes process framework to better reproduce some empirical market characteristics. In particular, by introducing quadratic feedback effects inspired by the QARCH discrete time model we obtain a power law distribution for volatility as well as time skewness.

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The aim of this thesis is to deepen the academic knowledge on the joint variations of high-frequency financial assets by analyzing them from a novel perspective. We take advantage of a tick-by-tick price database to highlight new stylistic facts about high-frequency correlation, and also to test the empirical validity of multivariate models. In Chapter 1, we discuss why high-frequency correlation is of paramount importance to trading. Furthermore, we review the empirical and theoretical literature on correlation at small time scales. Then we describe the main characteristics of the dataset we use. Finally, we state the results obtained in this thesis. In chapter 2, we propose an extension of the subordination model to the multivariate case. It is based on the definition of a global event time that aggregates the financial activity of all the assets considered. We test the ability of our model to capture notable properties of the empirical multivariate distribution of returns and observe convincing similarities. In Chapter 3, we study high-frequency lead/lag relationships using a correlation function estimator fit to tick-by-tick data. We illustrate its superiority over the standard correlation estimator in detecting the lead/lag phenomenon. We draw a parallel between lead/lag and classical liquidity measures and reveal an arbitrage to determine the optimal pairs for lead/lag trading. Finally, we evaluate the performance of a lead/lag based indicator to forecast short-term price movements. In Chapter 4, we focus on the seasonal profile of intraday correlation. We estimate this profile over four stock universes and observe striking similarities. We attempt to incorporate this stylized fact into a tick-by-tick price model based on Hawkes processes. The model thus constructed captures the empirical correlation profile quite well, despite its difficulty to reach the absolute correlation level.

This work is situated in the framework of the general diffusion equilibrium. We recall in the first chapter the immense richness of the relations obtained in this framework, in order to underline that the results are very closely linked to the modeling of the chosen behavior. The current trend in this area of economics and finance is to move towards greater finesse in the modeling of utility functions, in order to obtain results consistent with the observed macroeconomic series, which are currently poorly explained by the models. The aim of this work is to examine the impact of the relaxation of an assumption long used even implicitly in the models, called additivity or separability of the utility function. We shall see in the first chapter that the relaxation of this intuitively very questionable hypothesis destroys the condition of the classical envelope, which allows us, even in the simple model of Merton (1969), to find results that are more consistent with empirical tests: consumption is no longer proportional to wealth with a constant factor (Sundaresan (1990)). In the remaining chapters, we examine how this result can be extended to the most general economy possible. The first step in our approach, which corresponds to chapter 2, is to identify the extent to which the very general results of the Cox, Ingersoll et al.