arXiv subjects

Mehdi Tomas

Publications and source records attributed to Mehdi Tomas.

6 recordsLinked to original sources

arXiv2022

How to build a cross-impact model from first principles: Theoretical requirements and empirical results

Trading a financial instrument pushes its price and those of other assets, a phenomenon known as cross-impact. To be of use, cross-impact models must fit data and be well-behaved so they can be applied in applications such as optimal trading. To address these issues, we introduce a set of desirable properties which constrain cross-impact models. We classify cross-impact models according to which properties they satisfy and stress them on three different asset classes to evaluate goodness-of-fit. We find that two models are robust across markets, but only one satisfies all desirable properties and is appropriate for applications.

q-fin.TR↗

arXiv2022

Cross impact in derivative markets

Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. The empirical estimation of this effect on complex financial instruments, such as derivatives, is an open problem. To address this, we consider a setting in which the prices of derivatives is a deterministic function of stochastic factors where trades on both factors and derivatives induce price impact. We show that a specific cross-impact model satisfies key properties which make its estimation tractable in applications. Using E-Mini futures, European call and put options and VIX futures, we estimate cross-impact and show our simple framework successfully captures some of the empirical phenomenology. Our framework for estimating cross-impact on derivatives may be used in practice for estimating hedging costs or building liquidity metrics on derivative markets.

q-fin.TR↗

arXiv2021

A characterisation of cross-impact kernels

Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisations for trading purposes. We focus on kernels that guarantee that prices are martingales and anticipate future order flow (martingale-admissible kernels) and those that ensure there is no possible price manipulation (no-statistical-arbitrage-admissible kernels). We determine the overlap between these two classes and provide formulas for calibration of cross-impact kernels on data. We illustrate our results using SP500 futures data.

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arXiv2019

From microscopic price dynamics to multidimensional rough volatility models

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

q-fin.MF↗

arXiv2019

Deep Learning Volatility

We present a neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models -including the rough volatility family- and a range of derivative contracts. The aim of neural networks in this work is an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. We highlight how this perspective opens new horizons for quantitative modelling: The calibration bottleneck posed by a slow pricing of derivative contracts is lifted. This brings several numerical pricers and model families (such as rough volatility models) within the scope of applicability in industry practice. The form in which information from available data is extracted and stored influences network performance: This approach is inspired by representing the implied volatility and option prices as a collection of pixels. In a number of applications we demonstrate the prowess of this modelling approach regarding accuracy, speed, robustness and generality and also its potentials towards model recognition.

q-fin.MF↗

arXiv2019

On deep calibration of (rough) stochastic volatility models

Techniques from deep learning play a more and more important role for the important task of calibration of financial models. The pioneering paper by Hernandez [Risk, 2017] was a catalyst for resurfacing interest in research in this area. In this paper we advocate an alternative (two-step) approach using deep learning techniques solely to learn the pricing map -- from model parameters to prices or implied volatilities -- rather than directly the calibrated model parameters as a function of observed market data. Having a fast and accurate neural-network-based approximating pricing map (first step), we can then (second step) use traditional model calibration algorithms. In this work we showcase a direct comparison of different potential approaches to the learning stage and present algorithms that provide a suffcient accuracy for practical use. We provide a first neural network-based calibration method for rough volatility models for which calibration can be done on the y. We demonstrate the method via a hands-on calibration engine on the rough Bergomi model, for which classical calibration techniques are diffcult to apply due to the high cost of all known numerical pricing methods. Furthermore, we display and compare different types of sampling and training methods and elaborate on their advantages under different objectives. As a further application we use the fast pricing method for a Bayesian analysis of the calibrated model.

q-fin.MF↗