Stochastic supply curves and liquidity costs: estimation for brazilian equities

Abstract

Market Liquidity is characterized by the easiness and freedom to trade assets at desired volumes and for prices perceived as representative of their values. When there is a scarcity of bid and ask offers at those terms, traders face the so called Market Liquidity Risk and they must offer concessions on their original offers, leading to additional costs. Approaches to model this phenomena exist in broad variety but a common component of most Market Liquidity models is an instantaneous cost component, also known as transaction/execution costs or realized/instantaneous impact. This element, here the Liquidity Cost, gives the actual trading prices faced by a trader, frequently a deviation from the unobservable “true price”, normally represented as a GBM with the mid-price as a proxy for modeling purposes. Although it is clear that Liquidity Costs are a relevant aspect of Market Liquidity Risk and it is present in many models, it is relegated to a more simplistic treatment, being though as well-behaved, deterministic, smooth and static. The main point of this work is to follow a different approach by evaluating Liquidity Costs at a microstructural level by estimating the Stochastic Supply Curve from C¸ etin-Jarrow-Protter Model for Brazilian equities. To do so, high-frequency-data from B3’s ftp is used and to build Limit Order Books for several stocks at intraday periods. The empirical findings support the existence of non-trivial Stochastic Supply Curves as a representation for Liquidity Costs in several equities on Brazilian Markets. Additionally, there is evidence that Liquidity Costs may behave in contrast with some of the literature, being stochastic with time-varying functional representations on the LOB and with liquidity parameters that could be represented as mean-reverting stochastic process.