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The Multivariate price formation process and cross-impact

Abstract : This thesis comprises six parts. The first relates anonymous order flow and price changes using static, linear cross-impact models. We list desirable properties of such models, characterise those which satisfy them and test their predictions on different markets. The second part extends this approach to derivatives to obtain a tractable estimation method for cross-impact which is applied to SP500 options and VIX futures. In the third part, we generalise the previous setup to derive and estimate cross-impact models which account for the influence of past trades on current prices. The fourth part uses meta-order databases on stocks and futures to propose a formula for cross-impact which generalises the square-root law of market impact. In the fifth part, we propose a tick-by-tick model for price dynamics using Hawkes processes. We investigate scaling limits of prices in the high endogeneity regime to derive multivariate macroscopic price dynamics of rough Heston type. Finally, the last part solves the calibration problem of volatility models using neural networks.In the first part, we study linear cross-impact models which relate asset prices to anonymous order flow. These models are functions of the covariances of these variables. We introduce properties models should satisfy to behave well across market conditions and show that there exists a unique model which satisfies all such properties. We apply models on stocks and futures and find that the latter model is one of two robust across markets. Thus, it is a good candidate model for a unifying view of the price formation process on stocks and futures.The second part leverages the candidate model identified in the first part to extend the previous setup to derivatives. We derive an estimation method for the large cross-impact matrix which depends on low-dimensional covariances. Using SP500 options and VIX futures data, we show cross-impact captures salient features of the price formation process on derivatives.The second part examines cross-impact kernels, which account for the lasting influence of past trades on current prices. We focus on two kernel classes: kernels that anticipate future order flow to set martingale prices and those that prevent statistical arbitrage. We show that there is at most one kernel belonging to both classes. This kernel sets martingale prices but may not prevent arbitrage. To fix this, we introduce a methodology to obtain a second kernel which prevents statistical arbitrage and is the closest to setting martingale prices. Finally, we derive a calibration methodology for both kernels and apply it to futures data.The third part measures cross-impact from using two databases of proprietary orders sent by asset managers on U.S stocks and futures. These databases allow us to study the cross-impact of individual investor orders. We propose a formula for cross-impact which generalises the square-root law to account for price and order correlations. On both stocks and futures, we find that this generalisation gives more precise predictions than the square-root law.In the fourth part, we model the tick-by-tick price process using Hawkes processes. To capture the high endogeneity of financial markets, we investigate the limit where the L¹ norm of the spectral radius of the Hawkes kernel goes to one. We show that some multivariate rough volatility models emerge as the macroscopic limit of the microscopic price dynamics. In these models, volatility is a combination of underlying variance factors, each driven by a fractional Brownian motion of common Hurst index.Finally, the last part examines the calibration of volatility models by using neural networks. We first approximate the map from model parameters to contract prices using neural networks. This approximation can then be used to recover model parameters given market prices of contracts. We highlight the applicability of the method using synthetic and real market data.
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Submitted on : Monday, May 9, 2022 - 4:46:11 PM
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Mehdi Tomas. The Multivariate price formation process and cross-impact. Trading and Market Microstructure [q-fin.TR]. Institut Polytechnique de Paris, 2022. English. ⟨NNT : 2022IPPAX021⟩. ⟨tel-03662930⟩

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