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https://ah.lib.nccu.edu.tw/handle/140.119/31218| 題名: | Implied Volatility Function - Genetic Algorithm Approach | 作者: | 沈昱昌 | 貢獻者: | 陳威光<br>江彌修 <br> 沈昱昌 |
關鍵詞: | 基因演算法 隱含波動度 Genetic Algorithm Implied Volatility Function |
日期: | 2004 | 上傳時間: | 14-九月-2009 | 摘要: | 本文主要探討基因演算法(genetic algorithms)與S&P500指數選擇權為研究對象，利用基因演算法的模型來估測選擇權的隱含波動度後，進而求出選擇權的最適價值，用此來比較過去文獻中利用Jump-Diffusion Model、Stochastic Volatility Model與Local Volatility Model來估算選擇權的隱含波動度，使原始BS model中隱含波動度之估測更趨完善。在此篇論文中，以基因演算法求估的選擇權波動度以0.052的平均誤差值優於以Jump-Diffusion Model、Stochastic Volatility Model與Local Volatility Model求出之平均誤差值0.308，因此基因演算法確實可應用於選擇權波動度之求估。 In this paper a different approach to the BS Model is proposed, by using genetic algorithms a non-parametric procedure for capturing the volatility smile and assess the stability of it. Applying genetic algorithm to this important issue in option pricing illustrates the strengths of our approach. Volatility forecasting is an appropriate task in which to highlight the characteristics of genetic algorithms as it is an important problem with well-accepted benchmark solutions, the models mention in the previous literatures mentioned above. Genetic algorithms have the ability to detect patterns in the conditional mean on both time and stock depend volatility. In addition, the stability test of the genetic algorithm approach will also be accessed. We evaluate the stability of the new approach by examining how well it predicts future option prices. We estimate the volatility function based on the cross-section of reported option prices one week, and then we examine the price deviations from theoretical values one week later. |
參考文獻: | 1. Ait-Sahalia Y., Wang Y., Yared F. (1998). “Do Option Markets Correctly Asses the Probabilities of Movements of the Underlying Asset?” Forthcoming, Journal of Econometrics. 2. Andersen L., Brotherton-Ratcliffe R. (1998). “The Equity OptionVolatility Smile: AFinite Difference Approach,” Journal of Computational Finance 1, 2, 5–38. 3. Andersen T., Benzoni L., Lund J. (1999). “Estimating Jump-Diffusions for Equity Returns,” Working Paper, Northwestern University and Aarhus School of Business. 4. Bakshi G., Cao C., Chen Z. (1997). “Empirical Performance of Alternative Option Pricing Models,” Journal of Finance 52, 2003–2049. 5. Bates D. (1996). “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies 9, 1, 69–107. 6. Black F., Scholes M. (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637–654 7. Das S., Foresi S. (1996). “Exact Solutions for Bond and Option Prices with Systematic Jump Risk,” Review of Derivatives Research 1, 7–24. 8. Dumas B., Fleming J., Whaley R.E. (1996). Implied Volatility Functions: Empirical Test, Working paper, National Bureau of Economic Research, Cambridge. 9. Dupire B. (1994). “Pricing with a Smile,” RISK Magazine January, 18–20. 10. Goldberg D., Deb K. (1991). “A comparative analysis of selection schemes used in genetic algorithms,” Foundations of Genetic Algorithms, San Francisco. 11. Goldberg D., Korb B., Deb K. (1989). “Messy genetic algorithms: Motivation, analysis, and first results,” Complex Systems 3, 5. 12. Heston S. (1993). “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies 6, 2, 327–343. 13. Holland J. H. (1975). “Adaption in Natural and Artificial Systems,” The University of Michigan Press. 14. Hull J, White A. (1987). “The Pricing of Options with Stochastic Volatilities,” Journal of Finance 42, 281–300. 15. Koza, J.R. (1992). “Genetic Programming: On the Programming of Computers by Means of Natural Selection,” MIT Press, Cambridge MA. 16. Lagnado R., Osher S. (1997). “Reconciling Differences,” RISK Magazine April, 79–83. 17. Merton R. (1976). “Option Pricing when Underlying Stock Returns are Discontinuous,” Journal of Financial Economics May, 125–144. 18. Rubinstein M. (1994). “Implied Binomial Trees,” Journal of Finance 49, 771–818. 19. Smith S. (1980). “A Learning System Based on Genetic Adaptive Algorithms,” Ph.D. dissertation. University of Pittsburgh. 20. Stein E, Stein J. (1991). “Stock Price Distributions with Stochastic Volatility: An Analytic Approach,” Review of Financial Studies 4, 4, 727–752. 21. Webster’s II. (1994). New Riverside University Dictionary, Houghton Mifflin Company. |
描述: | 碩士 國立政治大學 金融研究所 91352031 93 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0913520312 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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