Market impact: a systematic study of the high frequency options market

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, E., Bel Hadj Ayed, A., Husson, A. and Abergel, F., Market impact: A systematic study of limit orders. Mark. Microstruct. Liq., 2018, 3(3&4), 1850008.], 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.     

The LeChatelier-Samuelson principle revisited

Within the context of a linear Leontief model, the LeChatelier-Samuelson principle examines the effects of an increase in some final demand on the output levels under the constraint that the production of certain goods is held at its original value. The principle states that the increase in any output is larger when fewer output levels are kept constant. The present paper discusses bounds for such incremental changes, second-order effects, the consequences on the markets for the products with restricted output levels, and generalizations of the original assumptions.I would like to thank two anonymous referees for their helpful comments.     

On the generalization of Rao,Hartley and Cochran's scheme

Summary The problem considered in this paper is a generalization of the usual Rao, Hartley and Cochran (RHC) scheme. In the usual RHC scheme the population ofN units is randomly divided inton groups wheren is the size of the sample. In this paper we propose to divide the population under consideration into (n+k) random groups wherek is some positive integer. Then a sample ofn groups is selected by using simple random sampling without replacement (SRSWOR). The expressions for the unbiased estimator of population total, its variance and the unbiased estimate of variance have been obtained under the proposed sheme. The condition under which the proposed sheme is more efficient than the usual RHC scheme has also been investigated.     

On invariant parametric covariance families

Summary In this note we characterize all linear transformations of random vectors which are invariant for a given parametric covariance family. Two one-dimensional covariance families are discussed in detail.