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博碩士論文 etd-0705112-115137 詳細資訊
Title page for etd-0705112-115137
論文名稱
Title
亞式選擇權定價之Black-Scholes方程的解析方法
Analytic Approaches to the Pricing Black-Scholes Equations of Asian Options
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
24
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2012-06-29
繳交日期
Date of Submission
2012-07-05
關鍵字
Keywords
Black-Scholes方程式、亞式平均期權、風險中性、計價轉換、馬可夫性質
Black-Scholes equation, change of Numeraire, risk neutral, Asian option, Markov property
統計
Statistics
本論文已被瀏覽 5757 次,被下載 846
The thesis/dissertation has been browsed 5757 times, has been downloaded 846 times.
中文摘要
亞式平均價格期權是一種收益函數與風險資產平均價格有關的期權,但目前尚未找出此期權的價格的封閉解。雖然無封閉解,但是仍可利用變數代換及計價轉換等方法,來簡化亞式平均價格期權所滿足的微分方程。本論文我們會說明亞式平均期權的性質以及簡化其所滿足微分方程的過程。
Abstract
Asian option is an option which payoff depends on the average underlying price over some some specific time period. Although there is no closed form solution of asian option, appropriate change of variable and Num’eraire would reduce some terms of equation satisfies the Asian call price function. This thesis presents asian option’s properties and process of reduction terms.
目次 Table of Contents
致謝 i
摘要 ii
Abstract iii
1 Introduction 1
2 The Black-Scholes Model......................................... 1
2.1 TheModel Setup.....................................................1
2.2 Risk-Neutral Valuation.............................................1
3 Asian Options............................................................3
3.1 Properties of Asian Option.......................................3
3.2 The Black-Scholes Equation for an Asian Option.......11
4 Numerical experiments...............................................14
5 Conclusion................................................................16
References...................................................................16
參考文獻 References
[1] J. E. Zhang, A semi-analytical method for pricing and hedging continuously sampled arithmetic average rate options, Journal of Computational Finance, 5 (2001), 59-79.

[2] Jan Veˇceˇr, A new PDE approach for pricing arithmetic average Asian options,Journal of Computational Finance, 4 (4), 105-113.

[3] L. C. G. Rogers AND Z. Shi, THE VALUE OF AN ASIAN OPTION, Journal of Applied Probability, 32, 1995, 1077-1088.

[4] William F. Ames NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. 3rd ed. 1992, Academic Press.

[5] Steven E. Shreve, Stochastic Calculus for Finance II Continuous-Time Models.2004, Springer.

[6] DuChateau, Paul, Applied partial differential equations. 2002, Mineola, N.Y. :Dover Publications
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