臺灣博碩士論文加值系統

本論文旨在探討在每日價格限制市場中，公司發放不連續現金股利對股票選擇權價值的數值解。我們由擴展Guo and Chang (2020)的單日股價機率密度函數至多天期的機率密度函數，並提出一個整合Haug et al. (2003) 及 Chang et al. (2016) 在每日價格限制的新效率定價架構，來考慮歐式選擇權於公司發放不連續現金股利的評價問題；此外，我們建立了一個結合了FFT的有效方法來計算漲跌幅限制下美式賣權提早履約之溢酬，並結合三點式Richardson外插法來計算美式賣權，最後我們也建構Monte Carlo模擬來驗證我們提出方法。

This study proposes a numerical solution for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day density function. Second, with the aid of the mulit-day density function, we use the framework of Haug et al.(2003) to value Euro-style equity option on stocks paying discrete dividends. Third, as for American options, we further adopt fast Fourier transform (FFT) to derive an efficient formula. We also employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed method is verified by a Monte Carlo simulation.

摘要... i
Abstract... ii
Table of Contents... iii
List of Tables... iv
List of Figures... v
1. Introduction... p.1
2. Literature Review... p.2
3. Model and Methodology... p.5
3.1 Framework of Haug et al.(2003)... p.5
3.2 Intraday characteristic function... p.11
3.3 Pricing option by fast Fourier transform(FFT)...p.14
3.4 Multi-day density function... p.15
3.5 Early exercise premium... p.15
4. Numerical Results and Findings... p.17
4.1 Numerical Results... p.17
4.2 Findings... p.20
5. Conclusion... p.21
References... p.23

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