本文根據以往研究經驗及觀察標準普爾 500 指數 (S&P500) 價格的變動趨勢，發現大部分選擇權的標的商品的價格並非總是很好地符合常態分配，並且常常具有偏斜及高峰、厚尾的特性，故本研究旨在放寬 B-S 模型背後的嚴謹假設，考慮服從偏斜常態分配的隨機誤差建構一個全新的選擇權評價模型，本研究將其稱為 Skew Normal 模型。並且選擇權的標的商品價格的波動率也並非始終為一個常數，因此又根據隱藏馬克夫模型推導出了另一個全新的選擇權評價模型，本研究將其稱為 Skew-Odmm 模型。並且以 2018 至 2019 年 S&P500 的價格走勢為實證對象，驗證了相較於傳統的 B-S 模型，兩個新模型都會因為負偏度適當低估選擇權的權利金。且考慮了波動率的兩種狀態的 Skew-Odmm 模型相較於Skew Normal 模型獲得結果也有所差異。

According to the previous research experience and the price trend of the S&P 500 index, we find that the price of most target product of the options are not always well-aligned with the normal distribution, and often have the characteristics such as skew, peak and thick tail, so this study aims to relax the rigorous assumptions behind the B-S model and consider the random errors subject to skew normal distribution to construct a new option pricing model. This study calls it the Skew Normal model. And the volatility of the target product price of the options is not always a constant, so another new option pricing model is derived based on the hidden markov model, which is called Skew-Odmm model in this study. And with the price trend of S&P500 from 2018 to 2019 as an empirical object, it is verified that compared with the traditional B-S model, the two new models will appropriately underestimate the premium of the option due to negative skewness. And the Skew-Odmm model, which takes into account the two states of volatility, has different results compared with the Skew Normal model.

陳松男， (2002) 。金融工程學：金融商品創新選擇權理論。出版地：華泰文化。

黃怡佳 (2006) ，選擇權評價模型之實證分析——以台指選擇權及 S&P500 選擇權為例，國立高雄應用科技大學

陳峙儒 (2004) S&P500 股價指數期貨與現貨間價格預測效果的探討 ---根據時間序列與人工智慧模型，國立成功大學

馬毓駿 (1999) ，馬克夫轉換模型在投資策略上的應用，國立政治大學

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 2, 171-178.

Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International economic review, 885-905.

Harvey, C. R., & Whaley, R. E. (1991). S&P 100 index option volatility. The Journal of Finance, 46(4), 1551-1561.

Chan, K., Chan, K. C., & Karolyi, G. A. (1991). Intraday volatility in the stock index and stock index futures markets. The Review of Financial Studies, 4(4), 657-684.

Chiras, D. P., & Manaster, S. (1978). The information content of option prices and a test of market efficiency. Journal of Financial Economics, 6(2-3), 213-234.

Lee, J. H., & Linn, S. C. (1994). College of Business Administration University of Oklahoma. The Review of Futures Markets, 13, 1.

Owen, D. B. (1956). Tables for computing bivariate normal probabilities. The Annals of Mathematical Statistics, 27(4), 1075-1090.

Goodwin, T. H. (1993). Business-cycle analysis with a Markov-switching model. Journal of Business & Economic Statistics, 11(3), 331-339.

Chen, S. N., Hsu, P. P., & Liang, K. Y. (2019). Option pricing and hedging in different cyclical structures: a two dimensional Markov-modulated model. The European Journal of Finance, 25(8), 762-779.

Neely, C., Weller, P., & Dittmar, R. (1997). Is technical analysis in the foreign exchange market profitable? A genetic programming approach. Journal of financial and Quantitative Analysis, 405-426.

Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of finance, 52(5), 2003-2049.

Corrado, C., & Su, T. (1998). An empirical test of the Hull‐White option pricing model. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 18(4), 363-378.