How much market making does a market need?

0496577 - ÚTIA 2019 RIV GB eng J - Článek v odborném periodiku
Peržina, V. - Swart, Jan M.
How much market making does a market need?
Journal of Applied Probability. Roč. 55, č. 3 (2018), s. 667-681. ISSN 0021-9002. E-ISSN 1475-6072
Grant CEP: GA ČR(CZ) GA15-08819S
Institucionální podpora: RVO:67985556
Klíčová slova: continuous double auction * limit order book * Stigler-Luckock model * rank-based Markov chain
Obor OECD: Pure mathematics
Impakt faktor: 0.610, rok: 2018
http://library.utia.cas.cz/separaty/2018/SI/swart-0496577.pdf

We consider a simple model for the evolution of a limit order book in which limit orders of unit size arrive according to independent Poisson processes. The frequencies of buy limit orders below a given price level, respectively sell limit orders above a given level, are described by fixed demand and supply functions. Buy (respectively, sell) limit orders that arrive above (respectively, below) the current ask (respectively, bid) price are converted into market orders. There is no cancellation of limit orders. This model has been independently reinvented by several authors, including Stigler (1964), and Luckock (2003), who calculated the equilibrium distribution of the bid and ask prices. We extend the model by introducing market makers that simultaneously place both a buy and sell limit order at the current bid and ask price. We show that introducing market makers reduces the spread, which in the original model was unrealistically large. In particular, we calculate the exact rate at which market makers need to place orders in order to close the spread completely. If this rate is exceeded, we show that the price settles at a random level that, in general, does not correspond to the Walrasian equilibrium price.
Trvalý link: http://hdl.handle.net/11104/0289345