買賣價差成本包含訂單成本、存貨成本及資訊不對稱成本。本論文以選擇權避險的觀念對真實價格的存貨成本建立模型，以持有買權(call) 或賣權 (put) 部位去規避持有股票部位或現金部位所承擔的風險成本。由於市場上無法觀測到每筆交易是否與具有私有資訊者交易，故文中將擁有私有資訊的交易事件視為一個隱藏變數(latent variable)。我們以期望值最大化演算法(EM algorithm) 去估計每筆交易與私有資訊者交易的相關參數。模擬分析中，以各種不同的參數模型去模擬生成資料，再以期望值最大化演算法估計參數並探討每一參數的收斂性。在實證結果中我們分析紐約證券交易所的高頻資料結果發現，如果股價報酬符合常態分配，則本文中的模型可得到較合理的參數估計。

The bid-ask spread costs consist of three components, which include order processing costs, inventory-holding costs, and adverse selection costs. In this paper, we model the inventory-holding costs of the bid-ask spread by option hedging. Theinventory-holding costs are hedged by call or put option positions. Since trades deal with the adverse selection traders are unobservable. We treat it as a latent variable, and Expected-Maximization (EM) algorithm are applied to estimate the related parameters of the model. Simulation studies are performed for several different
models. Empirical results of NYSE high frequency data show that the proposed model are obtain appropriate parameter estimation when the returns satisfied normality assumption.

第一章 導論............................................................................................1
第二章 文獻回顧....................................................................................3
第三章 模型推導....................................................................................8
第四章 模擬分析..................................................................................12
第五章 實證分析..................................................................................15
參考文獻...................................................................................................19
附錄一 期望值-最大化運算法(EM ALGORITHM)推導.................20
附錄二 股票代號對照表......................................................................23
附錄三 股價變動的KURTOSIS 與 SKEWNESS 圖.......................24
附錄四 原始資料型態節錄..................................................................27

Richard Roll. (1984). A Simple Implicit Measure of the Effective Bid-Ask Spread In
an Efficient Market. Journal of Finance 39, 1127-39.
Hans R. S. (1989). Inferring the Components of the Bid-Ask Spread: Theory and
Empirical Tests.” The Journal of Finance 44, 115-134.
Thomas J. G., Gautam K. and M. N. (1991) Estimation of the Bid-Ask Spread and
it’s Components: A New Approach. The Review of Financial Studies 4, 623-656.
Roger D. H. and Hans R. S. (1997). The Components of the Bid-Ask Spread: A
General Approach. The Review of Financial Studies 10, 995-1034.
Nicolas P.B., Bollen, T. S. and Robert E. W. (2004) Model the bid/ask spread:
measuring the inventory-holding premium. Journal of Financial Economics 72,
97-141.