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研究生:廖士豪
研究生(外文):Shi-Hau Liao
論文名稱:美式選擇權評價與內插
論文名稱(外文):American options pricing and Interpolation
指導教授:呂育道呂育道引用關係
指導教授(外文):Yuh-Dauh Lyuu
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:財務金融學研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:33
中文關鍵詞:美式選擇權內插
外文關鍵詞:American options pricingInterpolation
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以內插法加速美式選擇權的評價
Abstract
Pricing European and American options accurately and efficiently has been a main
concern in many studies. Although the closed-form solution of the European option
has already been derived by Fischer Black, Myron Scholes, and Robert Merton and
efficient numerical approximation algorithms are available, there are numerical meth-ods
that price such options with a much smaller cost and within acceptable error
bounds by use of some precomputation.
In the thesis, the method is proposed to build a look-up table for European and
American option values by precomputation. Once this is done, the requested option
value is then interpolated from the table via polynomial interpolation or cubic spline.
Though it takes time to build up the table, since the calculation is done off-line
and once and for all, the cost is fixed and can be amortized. More importantly, the
interpolated option value can be calculated very fast.
1 Introduction 1
2 Backrounds 3
2.1 Derivatives Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Option Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Payoffs on Standard Options . . . . . . . . . . . . . . . . . . . 4
2.2 Pricing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 The Balck-Scholes Formula . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Binomial Option Pricing Model . . . . . . . . . . . . . . . . . 7
3 Polynomial and Cubic Spline Interpolation 9
3.1 Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Cubic Spline Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Interpolation in Two or More Dimensions . . . . . . . . . . . . . . . . 13
3.4 Comparison Between Polynomial and Cubic Spline Interpolation . . . 14
3.4.1 Computational complexity . . . . . . . . . . . . . . . . . . . . 14
3.4.2 Polynomial wiggle problem . . . . . . . . . . . . . . . . . . . . 19
4 Numerical Results 22
4.1 Building Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Conclusion 32
Bibliography 33
Bibliography
[1] Lee W. Johnson and R. Dean Riess. Numerical Analysis. Addison-Wesley,
1982.
[2] Melvin J. and Maron. Numerical Analysis: A Pratical Approach. Macmillan,
1982.
[3] William H. Press., Saul A. Teukolsky, William T. Vetterling, and
Brian P. Flannery Numerical Recipes in C. Cambridge, 1992.
[4] L.C.G.Rogers and D. Taylay. Numerical Methods in Finance. Prentice-Hall,
2000.
[5] Hull, John. Options, Futures, and Other Derivatives. 4th edition. Cambridge,
1997.
[6] Yuh-Dauh Lyuu “Financial Engineering and Computation.” Cambridge, 2002.
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