Spread, volatility, and volume relationship in financial markets and market maker’s profit optimization Jack Sarkissian Managing Member, Algostox Trading LLC email:
[email protected] Abstract We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve price accuracy and reduce spread, but after some point additional liquidity begins to deteriorate price. The model allows to connect the bid-ask spread and high-low bars to measurable microstructural parameters and express their dependence on trading volume, volatility and time horizon. Using the established relations, we address the operating spread optimization problem to maximize the market-maker’s profit. 1. Introduction When discussing security prices it is customary to describe them with single numbers. For example, someone might say price of Citigroup Inc. (ticker “C”) on April 18, 2016 was $45.11. While good enough for many uses, it is not entirely accurate. Single numbers can describe price only as referring to a particular transaction, in which 푁 units of security are transferred from one party to another at a price $푋 each. Price could be different a moment before or after the transaction, or if the transaction had different size, or if it were executed on a different exchange. To be entirely accurate, one should specify these numerous details when talking about security price. We will take this observation a step further. Technically speaking, other than at the time of transaction we cannot say that price exists as a single number at all.