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博碩士論文 etd-0919107-133727 詳細資訊
Title page for etd-0919107-133727
論文名稱
Title
喜馬拉雅選擇權的定價與避險研究
Valuation and hedging of Himalaya option
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
39
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
2007-07-30
繳交日期
Date of Submission
2007-09-19
關鍵字
Keywords
選擇權避險、選擇權定價、山型選擇權、喜馬拉雅選擇權
Option hedging, Option Pricing, Himalaya Options, Mountain Range Options
統計
Statistics
本論文已被瀏覽 5729 次,被下載 25
The thesis/dissertation has been browsed 5729 times, has been downloaded 25 times.
中文摘要
選擇權第一次公開交易至今已有三十多年,隨時間進展,儘管交易所中進行交易的仍是以歐式選擇權為主,但歷經多年演變,歐式選擇權已不符合人們的需求,新奇選擇權於焉誕生。同樣地,選擇權的定價方式,也從傳統的(在Black-Scholes假設下的)公式解,到現在常用的二項樹、有限差分,亦或是本文所採用的蒙地卡羅模擬,其中主要的影響因素有下列兩點:第一,隨著選擇權合約複雜化-從單資產到多資產、從傳統歐式到路徑相依等,尋找選擇權的公式解顯得困難重重;第二,隨著個人電腦的發展,在個人電腦上進行數值運算已不再是一件遙不可及的事。也正是前面這兩個原因,配合著選擇權的發展,才會有今天這篇文章的誕生。喜馬拉雅選擇權亦屬新奇選擇權的一種,結合路徑相依及多資產的特色,傳統的公式解顯得無能為力,在多資產的情況下,二項樹及有限差分也將耗費大量計算時間,所以這是本文採用蒙地卡羅模擬的原因。
本文以蒙地卡羅模擬對喜馬拉雅選擇的定價為主,其中旁及不同變異數降低技巧的採用,這是因為蒙地卡羅模擬運用的良莠,其中一個關鍵因素就是比較相同的模擬次數下,估計值變異數的大小,較小的變異數會有較佳的效率,換言之,可以用較少的模擬次數獲得相同的誤差水準。最後,當定價完成,我們試圖對喜馬拉雅選擇權的避險做一簡單的探討。
Abstract
The first option has been publicly traded for more than 30 years. With the progress of time, despite the European option is still the exchange-traded option. But evolved through the years, the European option has not meet people's needs, so exotic option was born. Similarly, the pricing model, from the traditional closed-form solution (under the Black-Scholes assumption), now commonly used binomial trees, finite difference, or by using the Monte Carlo simulation. The main impact of the following factors: the first, with the complexity of the option contract - from single asset to multi-assets, from the plain vanilla option to the path-dependent option, it is more difficult to find the closed-form solution of the option. Second, with the development of personal computers, making numerical computing is no longer a difficult task. It is precisely these two front reason, there will be the birth of this article. Himalaya option is also an exotic options. With the multi-assets and path dependent features, we want to find a closed-form solution is very difficult. Under multi-assets situation, the binomial tree and finite difference will be time-consuming calculation. Therefore, this paper is using Monte Carlo simulation of reasons.
In this paper, we use Monte Carlo simulation to pricing Himalaya option, which includes several variance reduction techniques used to reduce sample variance. Finally, when pricing completed, we try to do a simple study to option hedging.
目次 Table of Contents
1. 前言 1
2. 喜馬拉雅選擇權及其定價型 3
3. 喜馬拉雅選擇權的定價 7
4. 喜馬拉雅選擇權的避險 19
5. 結論 20
參考文獻 References
Broadie, M., Glasserman, P. (1996), "Monte Carlo Methods for Security Pricing", Journal of Economic Dynamics $&$ Control, 21, pp. 1267-1321 .
Buhler, H. (2002), "Applying Stochastic Volatility Models for Pricing & Hedging Derivatives", Deutche Bank Global Quantitative Research Presentation.
Duan, J. C. (2003), "An Enhanced Path-Derivative Monte-Carlo Method for Computing Option Greeks" University of Toronto Working Paper.
Higham, Desmond J. (2004) An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, 1st. ed., London: Cambridge University Press.
Hull, John C. (2003). Options, Futures, and Other Derivatives. Prentice Hall Press.
Levy, G. (2002), “Multi-Asset Derivative Pricing Using Quasi-Random Numbers & Monte Carlo Simulation”, Numerical Algorithms Group.
Lewis, A. (2002), "The Mixing Approach to Stochastic Volatility & Jump Models", Wilmott Mag
Macaskill, J. (2001), "Managing the Downturn", Thomson IF Review.
Mahomed, O., Hnours Project of pricing Himalaya options, Univ. of the Witwatersrand, Johannesburg.
Overhaus, M. (2002), "Himalaya Options", Deutsche Bank Masterclass, Risk.net.
Quessette, R. (2002), "New Products, New Risks", Deutsche Bank Masterclass, Risk.net.
Ross, S. M. (2002), Simulation, 3th ed., Academic Press, New York.
張智星,(2000),MATLAB程式設計與應用,初版,新竹市:清蔚科技。
黃嘉斌,(1999),選擇權訂價公式手冊,初版,臺北市:麥格羅希爾。
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