看涨期权拍卖问题的精确解和渐近解
Exact and asymptotic solutions of the call auction problem
摘要：
集合竞价是一种广泛使用的交易机制，特别是在金融市场的开盘和收盘期间。在本文中，我们研究了一个标准的呼叫拍卖问题，订单提交根据泊松过程，随机价格分布根据一般分布，并可能在任何时候被取消。我们计算的分析表达式的交易量的分布，上下限的结算价格，和这些可能的结算价格的看涨拍卖的价格范围。利用顺序统计量理论的结果和具有独立随机指标的随机变量序列的极限定理，我们得到了所有这些分布的弱极限。在这种情况下，交易量和结算价格的边界被发现是渐近正态的，而结算价格的范围是渐近指数。这些分布的所有参数被明确地导出为传入订单流的参数的函数。
英文摘要：
The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.
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