Two Essays on Asian Option Valuation with Higher Moments in the Underlying Distribution

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許明峰(Ming-Feng Hsu) 查詢紙本館藏

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企業管理學系

論文名稱

(Two Essays on Asian Option Valuation with Higher Moments in the Underlying Distribution)

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摘要(中)

本研究主要目的是考量在標的資產之報酬分配具有高階動差的情況下，以數值模型評價亞洲選擇權，分為兩部分，第一部分針對歐式亞洲選擇權評價並與文獻結果做比較分析，第二部分則進一步討論美式亞洲選擇權之評價及其比較結果。
本研究首先以Edgeworth二項樹模型的上下限來評價歐式亞洲選擇權，我們證明，由Edgeworth二項樹模型評價亞洲選擇權的誤差界限是小於Chalasani et al.模型的誤差界限。此法用來評價各種不同偏態與峰態的亞洲外匯選擇權，評價的數值結果顯示，此方法能有效的處理標的資產報酬分配具有高階動差之權證，並且可以提供較過去其他的文獻為佳的選擇權估計值。
本研究接著以一個具有高階動差修正的Edgeworth二項樹模型，評價美式亞洲選擇權。與常態分配之標的資產比較，當時間階段(time steps)數增加時，我們的演算法是與Chalasani et al.一樣精確。若標的資產分配呈現負偏態及高峰態，則我們的權證估計值較Chalasani et al.來的精確，與Hull and White中作為比較基礎的估計值相似。數值分析顯示，在具有高階動差的標的資產分配中，修正之Edgeworth二項樹模型可以快速且精確地評價美式亞洲選擇權。

摘要(英)

The purpose of this study is to develop a numerical valuation model for Asian options while considering the higher moments of the underlying asset return distribution. Two issues are analyzed in the dissertation. First one discusses the pricing of European Asian options, and the second one extends the enquiry to American Asian options.
We first apply the Edgeworth binomial model with the lower and upper bounds to calculate the European Asian options. The error bound in our pricing from the Edgeworth binomial model is smaller than that from Chalasani et al. (1998). This method is then used to price the average rate currency options with different skewness and kurtosis. The numerical results show that our approach can effectively deal with the higher moments of the underlying distribution and provide better estimates of option value compared to various studies in literature.
We then develop a modified Edgeworth binomial model with higher moment consideration to price American Asian options. With lognormal underlying distribution for benchmark comparison, our algorithm is as precise as that of Chalasani et al. (1999), especially when the number of the time steps increases. If the underlying distribution displays negative skewness and leptokurtosis as often observed for stock index returns, our estimates are better than those in Chalasani et al. (1999) and very similar to the benchmarks in Hull and White (1993). The numerical analysis shows that our modified Edgeworth binomial models can quickly and accurately value American Asian options with higher moments in their underlying distribution.

關鍵字(中)

★ 高階動差
★ Edgeworth二項樹模型
★ 亞洲選擇權
★ 偏態
★ 峰態

關鍵字(英)

★ Edgeworth bino
★ Kurtosis
★ Asian options
★ Skewness

論文目次

ABSTRACT….……………………………………………..………Ⅲ
ACKNOWLEDGEMENTS……..…………………………………....Ⅶ
CONTENTS…………………………………………….………….IX
LIST OF FIGURES………………………………………………..XI
LIST OF TABLES………………………………………………...XII
Chapter 1. Introduction……………………………………………1
Chapter 2. Pricing European Asian Options with Skewness and Kurtosis in the Underlying Distribution…………… 3
2.1. Introduction to Chapter 2…………………………………3
2.2. Definitions and the Basic Binomial Model………………5
2.3. Edgeworth Binomial Model for Asian Option Valuation.8
2.4. Numerical Results………………………………………. 16
2.4.1. Valuation of European Asian Options under Normal Skewness and Kurtosis……………………………… 16
2.4.2. Valuation of European Asian Options under Various Skewness and Kurtosis……………………………… 19
2.5. Conclusion of Chapter 2…………………………………22
Chapter 3. Pricing American Asian Options with Higher moments in the Underlying Distribution……………………24
3.1. Introduction to Chapter 3…………………………… 24
3.2. Pricing Process of a Binomial Tree………………. 27
3.3. The Edgeworth Binomial Option Pricing Model………28
3.4. Upper Bound and Lower Bound…………………………. 32
3.5. Numerical Results……………………………………… 36
3.5.1. Comparisons of Price Estimates of American Asian Options under Lognormal Distribution…………… 36
3.5.2. Comparisons of Price Estimates of American Asian Options under Distributions with Higher Moments 39
3.6. Conclusion of Chapter 3………………………………. 41
Chapter 4. Conclusion……………………………………………42
References…………………………………………………………..43
Appendix for chapter 2: Analytical explanation for the Proposition……………………………………………. 51

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指導教授

王克陸、羅庚辛
(Kehluh Wang、Keng-Hsin Lo)

審核日期

2007-11-15

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