2019/04/05 by Rama Cont, Cont, Rama, Marvin S. Mueller +1 · 2 citations
Economics, Econometrics and Finance · #35R60 #60H15 #91B26 #91G80 #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1904.03058
openalex publication_date 2019/04/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We propose an analytically tractable class of models for the dynamics of a\nlimit order book, described through a stochastic partial differential equation\n(SPDE) with multiplicative noise for the order book centered at the mid-price,\nalong with stochastic dynamics for the mid-price which is consistent with the\norder flow dynamics. We provide conditions under which the model admits a\nfinite dimensional realization driven by a (low-dimensional) Markov process,\nleading to efficient estimation and computation methods. We study two examples\nof parsimonious models in this class: a two-factor model and a model with\nmean-reverting order book depth. For each model we analyze in detail the role\nof different parameters, the dynamics of the price, order book depth, volume\nand order imbalance, provide an intuitive financial interpretation of the\nvariables involved and show how the model reproduces statistical properties of\nprice changes, market depth and order flow in limit order markets.\n