<p style='text-indent:20px;'>We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We model demand using a two-parameter Brownian motion because (i) different points on the demand curve correspond to orders motivated by different information, and (ii) in general, the market price of risk equation of no-arbitrage theory has no solutions when the demand curve is driven by a finite number of factors, thus allowing for arbitrage. We prove that if the driving noise is infinite-dimensional, then there is no arbitrage in the model. Under the equivalent martingale measure, the clearing price is a martingale, and options can be priced under the no-arbitrage hypothesis. We consider several parameterizations of the model and show advantages of specifying the demand curve as a quantity that is a function of price, as opposed to price as a function of quantity. An online appendix presents a basic empirical analysis of the model: calibration using information from actual order books, computation of option prices using Monte Carlo simulations, and comparison with observed data.</p>

中文翻译：

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金融市场流动性的无限维模型

<p style='text-indent:20px;'>我们考虑流动性的动态市场模型，其中不匹配的买卖限价订单存储在订单簿中。由此产生的净需求面构成了模型的唯一输入。我们使用双参数布朗运动对需求进行建模，因为（i）需求曲线上的不同点对应于由不同信息驱动的订单，以及（ii）一般来说，无套利理论的风险方程的市场价格在以下情况下没有解需求曲线由有限数量的因素驱动，因此允许套利。我们证明，如果驱动噪声是无限维的，那么模型中就没有套利。在等价鞅测度下，清算价格为鞅，期权可以在无套利假设下定价。我们考虑了模型的几个参数化，并展示了将需求曲线指定为价格函数的数量，而不是价格作为数量函数的优势。在线附录介绍了该模型的基本实证分析：使用来自实际订单的信息进行校准，使用蒙特卡罗模拟计算期权价格，以及与观察到的数据进行比较。</p>