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研究生:戴全利
研究生(外文):Chuan-Li Tai
論文名稱:多重資產離散式障礙選擇權之評價
論文名稱(外文):Valuation of multiple-asset discrete barrier options
指導教授:王明隆王明隆引用關係
指導教授(外文):Andrew Ming-Long Wang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:財務金融研究所
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:2002
畢業學年度:90
語文別:中文
論文頁數:75
中文關鍵詞:離散式障礙選擇權積分方法兩資產
外文關鍵詞:two-assetintegral methoddiscrete barrier options
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摘 要

本研究之目的在透過數值積分方法來評價兩標的資產離散式障礙選擇權。一般評價單一資產離散式障礙選擇權之評價方法其缺點為: (1)“Barrier-too-close”,即所謂當標的資產價格接近障礙價格時,會產生較大的誤差。 (2)提高評價精確度時,須透過將靠近障礙價格之分割網格(mesh)切的非常細緻,但卻造成計算時間巨幅增加。 (3)計算時間隨著離散檢查點數目的增加呈指數成長,較不具效益性。
積分方法應用在多重資產離散式障礙選擇權,不但減少了誤差,更提高了計算效率。當標的資產價格接近障礙價格時,是採分段積分跳過該點,不但解決所謂“Barrier-too-close”之問題,更能克服多個離散障礙檢查點數目。而在計算時間上,隨著離散障礙檢查點數目的增加,所求得精確解所需之計算量也僅為障礙檢查次數之線性函數而非指數函數。
本文以兩資產最大值彩虹選擇權加上上升失效(up-and-out)障礙限制為例,透過參數簡化與單一資產下Black-Scholes之理論價格相比較,來確定模型方法之精確有用性,進而再評價兩資產離散障礙選擇權之理論價格。
ABSTRACT

Due to the barrier features, the prices of barrier options are less than standard or vanilla options. Therefore, the barrier options have become very popular products for managing exchange rate risk and are heavily traded on the OTC. In practice, barriers are typically observed discretely. There are essentially no closed-form solutions for pricing the discrete barrier options. The numerical approach for pricing the discrete barrier options would produce barrier-too-close problem. The risk-neutrality valuation algorithm would confront immense computational intenseness as the frequencies of discrete observations increase.
The recursive integral algorithm is proposed to price the discrete barrier options. The integral method can precisely estimate the value of barrier options even when the price of the underlying asset approaches the barrier levels. The computational time for finding a highly accurate numerical solution would be a linear function of the frequencies of discrete barrier observations.
Finally, the integral method is extended to value a two-asset discrete barrier options, and its static analysis is also presented.
目 錄
第一章 緒論……………………………………………………………1
第一節 研究背景與動機…………………………………………1
第二節 研究目的…………………………………………………4
第三節 研究架構…………………………………………………5

第二章 文獻探討………………………………………………………7
第一節 障礙選擇權之介紹………………………………………7
第二節 多重資產選擇權之介紹…………………………………10
第三節 文獻回顧…………………………………………………12

第三章 研究方法………………………………………………………20
第一節 兩資產一般型態之PDE………………………………….20
第二節 線性同質方程式…………………………………………23
第三節 積分方法之求解邏輯……………………………………26
第四節 數值積分方法……………………………………………29

第四章 實證模擬分析…………………………………………………37
第一節 評價兩資產最大值彩虹選擇權…………………………37
第二節 評價兩資產離散式障礙選擇權…………………………47
第三節 障礙選擇權契約之設計與評價…………………………58

第五章 結論與建議……………………………………………………66
附錄……………………………………………………………………69
參考文獻………………………………………………………………72
參考文獻
國外參考文獻
1.Ahn, D. S., Figlewski and B. Gao, (1999) “Pricing Discrete Barrier Options with an Adaptive Mesh Model.” Journal of Derivatives, 2, PP. 33-43
2.Boyle, P.P. and S.H. Lau, (1994) “Bumping Up Against the Barrier with the Binomial Method.” Journal of Derivatives, 2, pp. 6-14.
3.Boyle, P.P., and Y.K. Tse, (1990) “An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets.” Journal of Financial and Quantitative Analysis, 25, 215–227..
4.Broadie, M., P. Glasserman, and S. Kou, (1997) “A Continuity Correction for Discrete Barrier Options.” Mathematical Finance, 7, pp. 325-349.
5.Chang, C.C., S.L. Chang and B.S. Hsu, (2000): “Pricing Barrier Options Under Stochastic Volatility.” Journal of Financial Studies, 8, pp. 41-77.
6.Cheuk, T.H.F., and T.C.F. Vorst. (1996) “Complex Barrier Options.” Journal of Derivatives, 4, pp. 8-22.
7.Cox, J.C., and S. A. Ross. (1976) “The Valuation of Options for Alternative Stochastic Processes.” Journal of financial Economics, 3, pp.145-166.
8.Cox, J.C., S. A. Ross. , and M. Rubinstein (1979) “Option Pricing: A Simplified Approach.” Journal of financial Economics, 7, pp.229-264.
9.Heynen, P. and H. Kat, (1996) “Discrete Partial Barrier Options with a Moving Barrier.” Journal of Financial Engineering, 5 , pp. 199-209.
10.Johnson, H., (1987) “Options on the maximum or the minimum of several assets.” Journal of Financial and Quantitative Analysis. 22, 227–283.
11.Kou, S.G, (2001) “On Pricing of Discrete Barrier Options.” Working paper.
12.Kunitomo, N. and M. Ikeda (1992) “Pricing options with curved boundaries” Mathematical Finance, Vol. 2, Is. 4; pg. 275, 23 pgs.
13.Margrabe, W., (1978) “The value of an option to exchange one asset for another.” Journal of Finance. 33, 86–177.
14.Merton, R. C., (1973) “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, Vol. 4,141-183
15.Pooley, D.M., P. A. Forsyth, K. R. Vetzal, and R. B. Simpson, (2000)“An Unstructured Meshing for Two Asset Barrier Options.” Applied Mathematical Finance,7 ,pp. 33-60.
16.Reimer, M. and K. Sandmann (1995) “A discrete time approach for European and American barrier options.” Working paper.
17.Ritchken, P. (1995) “On pricing barrier options.” Journal of Derivatives, 3, pp.19-28.
18.Rubinstein, Mark, (1991) “Somewhere Over the Rainbow”, RISK 4, pp. 63-66
19.Rubinstein, M., and E. Reiner (1991): “Breaking Down the Barriers.”, RISK 4, pp. 28-35
20.Rubinstein, Mark, (1994) “Return to Oz”, RISK 7, pp. 67-71
21.Shen, Shih-yu, and Andrew M. L. Wang, (2001) “On Stop-Loss Strategies for Stock Investments”, Applied Mathematics and Computation, Vol. 119, P317-337.(U.S.A).
22.Smithson, C.W., (1998): Managing financial risk: a guide to derivative products, financial engineering, and value maximization, pp. 270-283.
23.Stulz, R.M., (1982) “Options on the minimum or the maximum of two risky assets: Analysis and applications.” Journal of Financial Economics, 10, 161–185.
24.Tian, Y., (1999) “Pricing Complex Barrier Options under General Diffusion Processes.” Journal of Derivatives, 4, pp. 11-30.
25.Topper, J., (1998) “Finite Element Modeling of Exotic Options.” Discussion Paper No. 216, University of Hannover, Version Dec. 27
26.Topper, J., (2001)“Worst Case Pricing of Rainbow Options” Discussion Paper No. 217
27.Wang, Andrew Ming-Long, Shih-Yu Shen, Chia-Chou Chiu, (2000) “The Pricing Model of the Reset Call Option”, The Sixth Asia Pacific Management Conference-The Great Asia in 21st Century, 247-254.
國內參考文獻
1.金修賢,民國八十七年,「蒙地卡羅模擬於美式彩虹選擇權之應用」,中央大學財務管理研究所碩士論文。
2.張傳章,張森林,許博翔,民國八十九年十二月,「隨機波動性下障礙選擇權之評價分析」,中國財務學刊,第八卷第三期,41-77頁。
3.寰宇證券投資顧問公司譯,民國八十八年,「金融風險管理: 衍生性產品-金融工程-價值最大化」,402-420頁。
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