控制變數法在數值選擇權評價模型之應用分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：6

、訪客IP：18.224.214.215

姓名

屈誠銘(Cheng-ming Chu ) 查詢紙本館藏

畢業系所

財務管理研究所

論文名稱

控制變數法在數值選擇權評價模型之應用分析
(Applying the Control Variate Technique to Numerical Option Pricing Models)

相關論文

★ 勞工退休金條例草案之轉換選擇權的評價與分析	★ 一般化的美式選擇權解析上界
★ 台灣加權指數波動率之實證研究	★ 蒙地卡羅模擬在選擇權評價上之運用
★ 固定匯率下跨國股酬交換之評價	★ 信用風險下可轉換公司債之評價
★ 跨通貨利率衍生性商品之評價與討論	★ GARCH選擇權評價模型：修正、應用和實證研究
★ 可轉換債券之定價與拆解	★ 高斯數值積分在選擇權評價上的應用研究
★ 指數期貨避險效率之比較：台灣與新加坡指數期貨市場之實證	★ 信用衍生性金融商品之研究:CB Asset Swap 及CDO
★ 選擇權價格之資訊內涵 --實際波動率與未來選擇權價格之預測	★ 選擇權實證研究:以臺指選擇權為例
★ 考慮交易成本與流動性風險成本下選擇權複製策略之比較	★ 選擇權實證研究-以S&P500指數選擇權為例

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

控制變數技術(control variate technique)是利用兩個相似的選擇權，一個無封閉解之選擇權當作被評價之選擇權，而另一個具有封閉解之選擇權來當控制變數，並利用此兩個選擇權在相同的數值方法下估計誤差會有具相關性，以增加估計無封閉解選擇權的效率。本論文主要是研究利用控制變數技術在蒙地卡羅模擬法評價無封閉解選擇權時，如何選擇最適的控制變數並檢驗蒙地卡羅模擬法是否可分辨出控制變數的優劣。
選擇好的控制變數可依循兩個原則:首先是找尋一選擇權與欲評價之選擇權滿足相同之偏微分方程式;其次是讓控制變數選擇權的邊界條件與欲評價之選擇權越相似越好。
文中將檢視不同型態之選擇權當作欲評價之選擇權包括:美式選擇權,障礙式選擇權,亞式選擇權,價差式選擇權。結果顯示在每一個例子中,選擇較佳的控制變數可以使控制變數法更加強蒙地卡羅模擬法的估計效率,此外也驗證出蒙地卡羅模擬法可以正確的區分出控制變數的優劣。

摘要(英)

For many complex options, analytical solutions are not available. In these cases a Monte Carlo simulation is an important numerical method. In its basic form, however, the Monte Carlo simulation is computationally inefficient, the control variate technique can be used to improve the efficiency of a Monte Carlo simulation. This paper presents a principle for finding better control variates when considering an option.
A good control variate has to satisfy two conditions: The first is that a good control variate satisfies the same PDE satisfied by the target option. The second is that the boundary condition for the control variate is similar to the boundary condition for the target option. Options under consideration in this paper include American put options, barrier options, Asian options, and spread options. The result shows that a good control variate can improve the efficiency of the simulation dramatically and a good control variate can be differentiated from a bad control variate in a Monte Carlo simulation.

關鍵字(中)

★ 亞式選擇權
★ 控制變數
★ 美式選擇權
★ 蒙地卡羅模擬法
★ 障礙式選擇權

關鍵字(英)

★ American option
★ Asian option
★ barrier option
★ control variate
★ Monte Carlo simulation
★ spread option

論文目次

Contents
1.Introduction……………………………………………………………….1
2.Methodology……………………………………………………………….5
2.1. Control Variate Technique ………………………………………….5
2.2.The Way to Find a Good Control Variate ………………….………. 9
3.Numerical Result …………………………………………………………11
3.1. American Put Option …………………………………………………11
3.2.Barrier Option …………………………………………..……………16
3.3.Asian Option …………………………………………………….…20
3.4.Spread Option ……………………………………………..…………23
4.Conclusion ………………………………………………………………26
5.Reference ………………………………………………………………37

參考文獻

References:
Barone-Adesi, G. and R. Whaley, (1987):”Efficient Analytical Approximation of American Option Values.” Journal of Finance, 42, pp.301-320.
Barraquand, J. and D. Martineau, (1995):”Numerical Valuation of High Dimensional Multivariate American Securities.” Journal of Financial and Quantitative Analysis, 30, pp. 383-405.
Boyle, P.P. (1977): ”Options: A Monte Carlo Approach.” Journal of Financial Economics, 4,pp. 323-338.
Derman, E., I. Kani, D. Ergener, and I. Bardhan, (1995):”Enhanced Numerical Methods for Options with Barriers.” Financial Analysts Journal, Nov-Dec, pp. 65-74.
Derman, E., I. Kani, D. Ergener, (1995):”Static Options Replication.” Journal of Derivatives, summer, pp. 78-95.
Geske, R. and H.E. Johnson, (1984):” The American Put Valued Analytically.” Journal of Finance, 39,pp. 1511-1524.
Haykov, J.M. (1993):”A Better Control Variate for Pricing Standard Asian Options.” Journal of Financial Engineering, 2, 3, pp. 207-216.
Hull, J. and A. White, (1988): "The Use of Control Variate Technique in Option-Pricing." Journal of Financial and Quantitative Analysis, 23, pp. 237-251.
Hull, J. and A. White, (1990): "Valuing Derivative Securities Using the Explicit Finite Difference Method." Journal of Financial and Quantitative Analysis, 23, 3, pp. 237-252.
Ingersoll, Jr. J.E. (1998):”Approximating American options and other financial contracts using barrier derivatives.” The Review of Financial Studies, 2, pp. 85-112.
Johnson, H. (1983): "An Analytical Approximation for the American Put Price." Journal of Financial and Quantitative Analysis, 18, pp. 141-148.
Johnson, H. (1987): "Options on the Maximum or the Minimum of Several Assets." Journal of Financial and Quantitative Analysis, 22, 3.
Ju, N. (1998): “ Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function.” The Review of Financial Studies, 3, pp. 627-646.
Kamna, A.G.Z. and A.C.F. Vorst, (1990):”A pricing method for options based on average asset values.” Journal of Banking and Finance,14, pp.113-129.
Kim, I.J. (1990):” The Analytical Valuation of American Options.” Review of Financial Studies, 3, pp. 547-572.
Longstaff, F.A. and E.S. Schwartz, (2001):” Valuing American Options by Simulation: A Simple Least-Squares Approach.” Review of Financial Studies, 14, pp. 113-147.
MacMillan, L.W. (1986):”An Analytical Approximation for the American Put Price.” Advances in Futures and Options Research, 1,pp. 119-139.
Merton, R.C. (1973):”Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4, pp. 141-183.
Omberg, E. (1987): “The valuation of American Puts with Exponential Exercise Policies.” Advances in Futures and Options Research, 2,pp. 117-142.
Rubinstein, M. and E. Reiner, (1991):”Breaking down the barriers.” Risk, 4, pp. 28-35.
Stulz, R. M. (1982): "Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications." Journal of Financial Economics, 10, pp. 161-185.
Tilly, J.A. (1993):” Valuing American Options in a Path Simulation Model.” Transactions of the Society of Actuaries, 45, pp. 83-104.
Turnbull, S. and L.M., Wakeman, (1991):”A quick algorithm for pricing European average options.” Journal of Financial and Quantitative Analysis, 26,pp. 371-389.

指導教授

張森林(San-Lin Chung)

審核日期

2001-6-30

推文