A stochastic partial differential equation model for limit order book dynamics
We propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise. We provide conditions under which the model admits a finite dimensional realization driven by a (low-...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2021
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| _version_ | 1826290411001348096 |
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| author | Cont, R Mueller, MS |
| author_facet | Cont, R Mueller, MS |
| author_sort | Cont, R |
| collection | OXFORD |
| description | We propose an analytically tractable class of models for the dynamics of a
limit order book, described as the solution of a stochastic partial
differential equation (SPDE) with multiplicative noise. We provide conditions
under which the model admits a finite dimensional realization driven by a
(low-dimensional) Markov process, leading to efficient methods for estimation
and computation. We study two examples of parsimonious models in this class: a
two-factor model and a model in which the order book depth is mean-reverting.
For each model we perform a detailed analysis of the role of different
parameters, study the dynamics of the price, order book depth, volume and order
imbalance, provide an intuitive financial interpretation of the variables
involved and show how the model reproduces statistical properties of price
changes, market depth and order flow in limit order markets. |
| first_indexed | 2024-03-07T02:43:46Z |
| format | Journal article |
| id | oxford-uuid:ab53c0a5-ebce-49ab-9ec5-1bf9aa60b8a0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:43:46Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:ab53c0a5-ebce-49ab-9ec5-1bf9aa60b8a02022-03-27T03:21:17ZA stochastic partial differential equation model for limit order book dynamicsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ab53c0a5-ebce-49ab-9ec5-1bf9aa60b8a0EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2021Cont, RMueller, MSWe propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise. We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation. We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean-reverting. For each model we perform a detailed analysis of the role of different parameters, study the dynamics of the price, order book depth, volume and order imbalance, provide an intuitive financial interpretation of the variables involved and show how the model reproduces statistical properties of price changes, market depth and order flow in limit order markets. |
| spellingShingle | Cont, R Mueller, MS A stochastic partial differential equation model for limit order book dynamics |
| title | A stochastic partial differential equation model for limit order book dynamics |
| title_full | A stochastic partial differential equation model for limit order book dynamics |
| title_fullStr | A stochastic partial differential equation model for limit order book dynamics |
| title_full_unstemmed | A stochastic partial differential equation model for limit order book dynamics |
| title_short | A stochastic partial differential equation model for limit order book dynamics |
| title_sort | stochastic partial differential equation model for limit order book dynamics |
| work_keys_str_mv | AT contr astochasticpartialdifferentialequationmodelforlimitorderbookdynamics AT muellerms astochasticpartialdifferentialequationmodelforlimitorderbookdynamics AT contr stochasticpartialdifferentialequationmodelforlimitorderbookdynamics AT muellerms stochasticpartialdifferentialequationmodelforlimitorderbookdynamics |