Black-Scholes選擇權定價模型是各種選擇定價的開山始祖，無論在理論或實務上均獲致許多的便利及好評，美中不足的是，這種既定模型下結構化參數的估計問題，在真實體系的結構訊息未知或是不明朗時，或是模式錯誤，亦或政治結構或金融環境不知時，該模型在實證資料的評價上會面臨價格偏誤的窘境。是故，許多的數值演算法（numerical algorithms）便因應而生，這些方法一則源於對此基本模型的修正，一則是屬於逼近的數值解。 評價選擇權的方法雖不一而足，然所有的這些理論或模型可分為二大類即模型驅動的理論（model-drive approach）及資料驅動的理論（data-driven approach）。前者是建構在許多重要的假設，當這些假設成立時，則選擇權的價格可用如Black-Scholes偏微分方程來表示，而後再用數值解法求算出，許多的數值方法即屬於此類的範疇；而資料驅動的理論（data-driven approach），其理論的特色是它的有效性（validity）不像前者是依其假設，職是之故，他在處理現實世界的財務資料時更顯見其具有極大的彈性。這些以計算智慧（computation intelligence）為主的財務計量方法，如人工神經網路（ANNs），遺傳演算法（GAs），遺傳規劃（GP）已在財務工程（financial engineering）領域上萌芽，並有日趨蓬勃的態勢，而將機器學習技術（machine learning techniques）應用在衍生性商品的定價，應是目前財務應用上最複雜及困難，亦是最富挑戰性的問題。 本文除了對現有文獻的整理評析外，在人工神經網路方面，除用於S&P 500的實證外，並用於台灣剛推行不久的認購構證評價之實證研究；而遺傳規劃在計算智慧發展的領域中，算是較年輕的一員，但發展卻相當的快速，雖目前在經濟及財務上已有一些文獻，但就目前所知的二篇文獻選擇權定價理論的文獻中，仍是試圖學習Black-Scholes選擇權定價模型，而本文則提出修正模型，使之成為完全以資料驅動的模型，應用於S&P 500實證，亦證實可行。最後，本文結合計算智慧中的遺傳演算法（ genetic algorithms）及數學上的加權殘差法（weight-residual method）來建構一條除二項式定價模型，人工神經網路定價模型，遺傳規劃定價模型等資料驅動模型之外的另一種具適應性學習能力的選擇權定價模式。 / The option pricing development rapid in recent years. However, the recent rapid development of theory and the application can be traced to the pathbreaking paper by Fischer Black and Myron Scholes(1973). In that pioneer paper, they provided the first explicit general equilibrium solution to the option pricing problem for simple calls and puts and formed a basis for the contingent claim asset pricing and many subsequent academic studies. Although the Black-Scholes option pricing model has enjoyed tremendous success both in practice and research, Nevertheless, it produce biased price estimates. So, many numerical algorithms have advanced to modify the basic model. I classified these traditional numerical algorithms and computational intelligence methods into two categories. Namely, the model-driven approach and the data-driven approach. The model-driven approach is built on several major assumptions. When these assumption hold, the option price usually can be described as a partial differential equation such as the Black-Scholes formula and can be solved numerically. Several numerical methods can be regarded as a member of this category. There are the Galerkin method, finite-difference method, Monte-Carlo method, etc. Another is the data-driven approach. The validity of this approach does not rests on the assumptions usually made for the model-driven one, and hence has a great flexibility in handling real world financial data. Artificial neural networks, genetic algorithms and genetic programming are a member of this approach. In my dissertation, I take a literature review about option pricing. I use artificial neural networks in S & P 500 index option and Taiwan stock call warrant pricing empirical study. On the other hand, genetic programming development rapid in recent three years, I modified the past model and contruct a data-driven genetic programming model. andThen, I usd it to S & P 500 index option empirical study. In the last, I combined genetic algorithms and weight-residual method to develop a option pricing model.

當線性模型中包含隨機效果項時，若將之視為固定效果或直接忽略，往往會造成嚴重的推測偏差，故應以混合線性模型為架構。若模式中只包含一個隨機效果項，則模式中有兩個變異數成份，若包含 個隨機效果項，則模式中有 個變異數成份。本論文主要在介紹至少兩個變異數成份時固定效果及隨機效果線性組合的最佳線性不偏推測量（BLUP），及其推測區間之推導與建立。然而BLUP實為變異數比率的函數，若變異數比率未知，而以最大概似法（Maximum Likelihood Method）或殘差最大概似法（Residual Maximum Likelihood Method）估計出變異數比率，再代入BLUP中，則得到的是經驗最佳線性不偏推測量（EBLUP）。至於推測區間則與EBLUP的均方誤有關，本論文先介紹如何求算其漸近不偏估計量，再介紹EBLUP之推測誤差除以 後，其自由度的估算方法，據以建構推測區間。 / When random effects are contained in the model, if they are treated as fixed effects or ignore, then it may result in serious prediction bias. Instead, mixed linear model is to be considered. If there is one source of random effects, then the model has two variance components, while it has variance components, if the model contains random effects. This study primarily presents the derivation of the best linear unbiased predictor (BLUP) of a linear combination of the fixed and random effects, and then the conduction of the prediction interval when the model contains at least two variance components. However, BLUP is a function of variance ratios. If the variance ratios are unknown, we can replace them by their maximum likelihood estimates or residual maximum likelihood estimates, then we can get empirical best linear unbiased predictor (EBLUP). Because prediction interval is relating to the mean squared error (MSE) of EBLUP, so the study first introduces how to get its approximate unbiased estimator, m_a , then introduces how to evaluate the degrees of freedom of the ratio of the prediction error for the EBLUP and m_a ^1/2 , in order to use both of them to establish the prediction interval.