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| Title: | 偏斜常態分配的隨機誤差與隱藏馬可夫鏈建構選擇權定價模型——以標準普爾500指數為例
Option Pricing Model with Skew Normal Random Error and Hidden Markov Chain: Evidence from the S&P500 |
| Authors: | 王楷文
Wang, Kai-Wen |
| Contributors: | 劉惠美
王楷文
Wang, Kai-Wen |
| Keywords: | 選擇權評價
偏斜常態分配
隱藏馬可夫模型
Option Pricing
Skew Normal Distribution
Hidden Markov Model |
| Date: | 2020 |
| Issue Date: | 2021-04-01 11:21:17 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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
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| Description: | 碩士
國立政治大學
統計學系
107354030 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0107354030 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202100390 |
| Appears in Collections: | [統計學系] 學位論文
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