Rigorous results for the Stigler-Luckock model for the evolution of an order book

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00490719" target="_blank" >RIV/67985556:_____/18:00490719 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1214/17-AAP1336" target="_blank" >http://dx.doi.org/10.1214/17-AAP1336</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/17-AAP1336" target="_blank" >10.1214/17-AAP1336</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rigorous results for the Stigler-Luckock model for the evolution of an order book

Popis výsledku v původním jazyce

In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching order arrives. Assuming stationarity, Luckock showed that the distribution functions of the best buy and sell order in the order book solve a differential equation, from which he was able to calculate the position of two prices Jc−<Jc+ such that buy orders below Jc− and sell orders above Jc+ stay in the order book forever while all other orders are eventually matched. We extend Luckock’s model by adding market orders, that is, with a certain rate traders arrive at the market that take the best available buy or sell offer in the order book, if there is one, and do nothing otherwise. We give necessary and sufficient conditions for such an extended model to be positive recurrent and show how these conditions are related to the prices Jc− and Jc+ of Luckock.

Název v anglickém jazyce

Rigorous results for the Stigler-Luckock model for the evolution of an order book

Popis výsledku anglicky

In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching order arrives. Assuming stationarity, Luckock showed that the distribution functions of the best buy and sell order in the order book solve a differential equation, from which he was able to calculate the position of two prices Jc−<Jc+ such that buy orders below Jc− and sell orders above Jc+ stay in the order book forever while all other orders are eventually matched. We extend Luckock’s model by adding market orders, that is, with a certain rate traders arrive at the market that take the best available buy or sell offer in the order book, if there is one, and do nothing otherwise. We give necessary and sufficient conditions for such an extended model to be positive recurrent and show how these conditions are related to the prices Jc− and Jc+ of Luckock.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Applied Probability

ISSN

1050-5164

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

45

Strana od-do

1491-1535

Kód UT WoS článku

000434140900006

EID výsledku v databázi Scopus

2-s2.0-85048045652