Market Impact: A Systematic Study of the High Frequency Options Market

Abstract

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders -large orders that are split into smaller pieces before being sent to the market -on one of the main Asian markets. In line with our previous work on the equity market [Said et al., 2018], we propose an algorithmic approach to identify metaorders, based on some implied volatility parameters, the at the money forward volatility and at the money forward skew. In both cases, we obtain results similar to the now well understood equity market: Square-root law, Fair Pricing Condition and Market Impact Dynamics.

How Option Hedging Shapes Market Impact

“…The relaxation phenomenon has been studied from an empirical point of view in stocks market [Bershova and Rakhlin, 2013] [Bacry et al, 2015] [Said et al, 2018 and with a theoretical insight in [Bouchaud et al, 2004] [Gatheral et al, 2011 and [Farmer et al, 2013] for instance. Recently the same has been done empirically concerning options market [Said et al, 2019]. Let us consider (dS n ) n∈N a metaorder starting from dS = 0, hence N (dS) = +∞.…”

“…To this end our approach is mainly inspired by the original definition of a metaorder which is nothing less than a large order split into several small orders to be executed incrementally. Besides it has been shown in two companion papers ([Said et al, 2018] and [Said et al, 2019]) that the metaorders can obey to an algorithmic definition. This implies that they are not necessarily driven by execution strategies but they are more often simply opportunistic or hedging trades.…”

“…We will denote by I the permanent impact of the metaorder (dS n ) n∈N . According to the Fair Pricing condition -predicted theoretically in [Farmer et al, 2013] and validated empirically in equity [Said et al, 2018] and options [Said et al, 2019] market -the permanent impact I satisfies the following identity:…”

“…In that case, the following re-hedging trades will be considered also small and we will show how this implies to consider at this scale local linear market impact rule. Indeed it is well established that the response to individual small orders are linear and it is only the aggregation of those small orders executed consecutively, better known as metaorders, which lead to concave market impact in agreement to a square-root law in the equity markets [Moro et al, 2009] [Bacry et al, 2015] [Toth et al, 2011 but also in the options market [Toth et al, 2016] [Said et al, 2019. The multi-timescale property of the market impact has also been recently adressed in [Benzaquen and Bouchaud, 2018].…”

Market Impact: Empirical Evidence, Theory and Practice

“…In recent years many studies on different markets have been conducted to understand the influence of metaorders on the price formation process: [Almgren et al, 2005] [Moro et al, 2009] [Toth et al, 2011] [Bershova and Rakhlin, 2013] [Bacry et al, 2015] [Gomes and Waelbroeck, 2015] [Said et al, 2017 for the stock market, [Said et al, 2021] for options market and for the bitcoin market. All of these studies agree that market impact is a two-phase process.…”