No-Arbitrage Implies Power-Law Market Impact and Rough Volatility

Jusselin, Paul; Rosenbaum, Mathieu

doi:10.2139/ssrn.3180582

Cited by 18 publications

(24 citation statements)

References 19 publications

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“…The latent limit order book model (LLOB), described, for example, in (Donier et al, 2015;Tóth et al, 2011), and the model based on Hawkes processes, in (Jusselin & Rosenbaum, 2020), provide two explanations of the concavity of price impact that are the closest to the one proposed herein. The LLOB model assumes the existence of a large number of potential buyers and sellers whose reservation prices for the asset follow a common stochastic process plus an idiosyncratic Brownian component independent across agents.…”

Section: Introduction and Main Resultsmentioning

confidence: 89%

“…The model of (Jusselin & Rosenbaum, 2020) (see also the references therein) starts by assuming that the order flow follows a self-exciting Hawkes process, which is defined by the associated kernel function, and that the price is driven only by the order flow (the latter is referred to as the noarbitrage condition in (Jusselin & Rosenbaum, 2020) and in preceding papers). Then, assuming that the price impact has a non-trivial resilience (i.e., the price process obtains a trend in the opposite direction to the meta-order, right after the execution), the authors of (Jusselin & Rosenbaum, 2020) show that the only kernel that produces a well defined price impact in the infinite-activity regime (i.e., with small orders arriving at a high rate) is the power function. The latter leads to a concave power-type price impact.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The latter leads to a concave power-type price impact. The argument of (Jusselin & Rosenbaum, 2020) is based on the properties of Hawkes process, one of the most important of which is the self-excitatory property. Even though the explanation of the concavity of price impact proposed herein is different, it is similar to (Jusselin & Rosenbaum, 2020) in that one of its main building blocks is the self-excitatory property of the fundamental price process, discussed further in this section.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

See 2 more Smart Citations

A simple microstructural explanation of the concavity of price impact

Nadtochiy

2021

Mathematical Finance

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This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e., the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co-directional trades is nonlinear and asymptotically concave. The main practical conclusion of the proposed explanation is that, throughout a meta-order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions, one of which can be tested, at least for large-tick stocks, using publicly available market data.

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Section: Introduction and Main Resultsmentioning

confidence: 89%

Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: Introduction and Main Resultsmentioning

confidence: 99%

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A simple microstructural explanation of the concavity of price impact

Nadtochiy

2021

Mathematical Finance

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“…We refer to [8, 12] for details about these three stylized facts. This Hawkes-based microscopic framework can easily account for other features of markets: for example [22] examines the issue of permanent market impact, [10] studies how a bid/ask asymmetry creates a negative price/volatility correlation, and the so-called Zumbach effect is considered in [7].…”

Section: Introductionmentioning

confidence: 99%

From microscopic price dynamics to multidimensional rough volatility models

Rosenbaum

Tomas

2021

Adv. Appl. Probab.

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Rough volatility is a well-established statistical stylized fact of financial assets. This property has led 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 accurately reproduce 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 in the multidimensional price formation process. In particular, we recover classical properties of high-dimensional stock correlation matrices.

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“…In turn, this has helped us understand key properties of dynamics of asset prices. For instance, market impact explains why price volatilities are well-modeled by rough fractional Brownian motions [15].…”

Section: Introductionmentioning

confidence: 99%

A characterisation of cross-impact kernels

Rosenbaum¹,

Tomas²

2021

Preprint

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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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No-Arbitrage Implies Power-Law Market Impact and Rough Volatility

Cited by 18 publications

References 19 publications

A simple microstructural explanation of the concavity of price impact

A simple microstructural explanation of the concavity of price impact

From microscopic price dynamics to multidimensional rough volatility models

A characterisation of cross-impact kernels

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