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題名:選擇權定價與風險值之蒙地卡羅財務計算模擬
書刊名:管理與資訊學報
作者:鄭為民枋志深
作者(外文):Jeng, Wei-minFang, Jhih-shen
出版日期:2007
卷期:12
頁次:頁129-153
主題關鍵詞:選擇權定價分析蒙地卡羅模擬平行處理風險值Option priceMonte Carlo simulationParallel processValue at risk
原始連結:連回原系統網址new window
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在選擇權領域相關研究中,選擇權定價分析的重要性日趨增加,選擇權定價分析已經有許多方法提出,如Black-Scholes定價模型,二項式評價以及有限差分法等不同模型;這些方法仍然存在若干缺點,如Black-Scholes定價模型是以固定的條件來做定價分析,但無法對新種類選擇權來進行評價,因此本文採用蒙地卡羅模擬於選擇權定價分析,其原理為使用選擇權評價公式以及隨機產生亂數,藉由電腦進行反覆模擬來計算選擇權的價值,模擬次數越多越接近實際選擇權價格,另外,為了計算選擇權在未來可能的損失,本文使用風險值衡量方法,同樣使用蒙地卡羅模擬來計算可能的損失,一般蒙地卡羅模擬的亂數產生方式,如線性同餘法(Linear Congruence Method),需要較多模擬次數才能使模擬平均值接近實際值,因此本文使用Sobol準亂數產生器(Quasi Random Number Generator)的蒙地卡羅模擬,來對選擇權作定價分析,在模擬次數較少的情況下,即可得到較準確數值。由於蒙地卡羅模擬需要重複運算多次來得到平均值,所以本實驗使用Compaq ProLiant DL380及SGI Altix350對稱多處理器(SMP)伺服器,配合軟體OpenMP函式庫,能夠有效的利用複數個處理器減少蒙地卡羅模擬計算時間。在本研究中並以圖形化使用者介面的系統,來對實際選擇權作計算以及計算風險值,此系統可以同時顯示多筆金融商品運算結果,結果發現蒙地卡羅模擬和其他選擇權定價分析方式比較,能精確的對選擇權價格進行評價。
In the realm of in the option price research, the importance of option price analysis is increasing day by day. Many option price analysis models have bee addressed, such as Black-Scholes option model, binomial option pricing method, and finite difference methods. However, there are known drawbacks to these proposed models. For example, the Black-Scholes option model uses the fixed formula to calculate the option price, but the model is unable to adapt to the latest stock option. This paper used an effective Monte Carlo simulation to take on the option price problem. The idea is to use both option price formula and a random number generator to conduct the simulation repeatedly of the option price. Close estimate of the option price can be obtained with vast amount of simulation times. Important Monte Carlo simulation like Linear Congruence methods demands significant number of simulation for generating good estimates. This paper uses Sobol random number generator to perform option price calculation for efficient and accurate results. Moreover, this study used Compaq ProLiant DL380 and SGI Altix symmetric multiple-processor machine together with the OpenMP library to reduce the overall Monte Carlo simulation time. A graphic user interface syst+em is provided for easy manipulation. Multiple financial derivatives can be analyzed in parallel in our program setup for achieving bets performance and the result demonstrates the superior performance comparing with other findings.
期刊論文
1.Joy, C.、Boyle, R.、Tan, K. S.(1996)。Quasi-Monte Carlo methods in numerical finance。Management Science,42,926-938。  new window
2.Bratley, Paul、Fox, Bennett L.(198803)。Algorithm 659: Implementing Sobol’s quasirandom sequence generator。ACM Transactions on Mathematical Software,14(1),88-100。  new window
3.Ito, K.(1951)。On Stochastic Differential Equation Memories。American Mathematical Society,4,1-51。  new window
4.Efron, B.(1979)。Bootstrap methods: Another look at the jackknife。The Annals of Statistics,7,1-26。  new window
5.Tilley, J. A.(1993)。Valuing American Options in a Path Simulation Model。Transactions of the Society of Actuaries,45,83-104。  new window
6.Boyle, Phelim P.、Broadie, Mark、Glasserman, Paul(1997)。Monte Carlo Methods for Security Pricing。Journal of Economic Dynamics and Control,21(8/9),1267-1321。  new window
7.Barraquand, J.、Martineau, D.(1995)。Numerical Valuation of High Dimensional Multivariate American Securities。Journal of Financial and Quantitative Analysis,30(3),383-405。  new window
8.Merton, Robert C.(1973)。Theory of Rational Option Pricing。Bell Journal of Economics and Management Science,4(1),141-183。  new window
9.Simons, Katerina(1996)。Value at Risk - New Approaches to Risk Management。New England Economic Review,Sep/Oct,3-13。  new window
10.Raymar, S.、Zwecher, M.(1997)。Monte Carlo Estimation of American Call Options on the Maximum of Several Stocks。The Journal of Derivatives,5(1),7-23。  new window
11.Black, F.、Scholes, M.(1973)。The Price of Option and Corporate Liabilities。Journal of Political Economy,81,637-659。  new window
學位論文
1.王姿云(2003)。可轉換公司債拆解訂價與實例分析(碩士論文)。國立中山大學。  延伸查詢new window
2.何振文(2000)。蒙地卡羅模擬在選擇權評價上之運用(碩士論文)。國立中央大學。  延伸查詢new window
3.邱紀尊(2001)。美式選擇權之數值演算法(碩士論文)。輔仁大學。  延伸查詢new window
4.魏湘芸(2004)。混合OpenMP及MPI的蒙地卡羅正子造影模擬(碩士論文)。東吳大學。  延伸查詢new window
圖書
1.李存修、台大財務金融研究所(1999)。台灣認購權證個案集「價格行為&避險操作」。臺北:智勝出版社。  延伸查詢new window
2.Joshi, Mark(2004)。C++ Design Patterns and Derivatives Pricing。Cambridge University Press。  new window
3.McDonald, Robert L.(2003)。Derivatives Markets。Addison Wesley Publishing Company。  new window
4.Brockhaus, Oliver、Farkas, Micheal、Ferraris, Andrew、Long, Douglas、Overhaus, Marcus(2000)。Equity Derivatives and Market Risk Models。Risk Publications。  new window
5.Marrison, Chris(2002)。The Fundamentals of Risk Measurement。New York, NY:McGraw-Hill Book Company。  new window
6.Jorion, P.(1997)。Value at Risk: The New Benchmark for Controlling Market Risk。McGraw-Hill。  new window
7.Jorion, Philippe(2000)。Value at Risk: The New Benchmark for Managing Financial Risk。Irvine:University of California。  new window
8.陳威光(2001)。選擇權:理論、實務與運用。臺北:智勝文化。  延伸查詢new window
9.Jackel, Peter(2002)。Monte Carlo Methods in Finance。New York, NY:John Wiley & Sons。  new window
10.Hull, J. C.(2002)。Options, Futures, and Other Derivatives。London:Prentice Hall。  new window
圖書論文
1.Benjamin, Jun、Kocher, Paul(1999)。The Intel Random Number Generator。White Paper Prepared For Intel Corporation。  new window
 
 
 
 
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