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研究生：	曾家慶 Tseng, Chia-Ching
論文名稱：	1-FSV模型和GARCH模型在波動率預測的比較 A Comparison of the 1-FSV and GARCH Models in Local Volatility Forecasts
指導教授：	王澤世 Wang, Alan, 李宏志 Lee, Hong-Chi
學位類別：	碩士 Master
系所名稱：	管理學院 - 財務金融研究所 Graduate Institute of Finance
論文出版年：	2006
畢業學年度：	94
語文別：	英文
論文頁數：	55
中文關鍵詞：	隱含波動率、GARCH 模型、1-FSV模型、DVF 、Volatility surface
外文關鍵詞：	Implied volatility, GARCH model, 1-FSV model, DVF, Volatility surface
相關次數：	點閱：131 下載：4
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本論文利用S&P500指數選擇權價格來比較不同模型下波動率預測的精確性.樣本資料為2003年九月到2004年六月,我們檢視1-FSV和GARCH模型在預測實際波動率上的預測能力.
實證結果顯示GARCH模型在預測能力上表現比1-FSV為佳,此外,我們利用隱含波動率函數繪製volatility surface用以呈現波動率和履約價及到期日之間的關係.

This paper compares the accuracy of different measures for forecasting the volatility of S&P 500 (SPX) index options prices. Using daily data reported daily by the CBOE from September 2003 through June 2004, we examine the predictive performance of volatilities of the 1-FSV and GARCH models and then contrast them with the realized volatilities obtained from S&P 500 index.

The results of our study suggest that the GARCH (1,1) model outperforms the 1-FSV model in terms of ex ante forecasting power of volatility. Besides, we plot the volatility surface to exhibit the relationship between implied volatility and exercise prices and time to maturities.

Chapter 1 Introduction………………………………………………………………1
1.1 Background………………………………………………………………………..1
1.2 Motivation and Purpose…………………………………………………………...2
1.3 Research Framework………………………………………………………………5
Chapter 2 Literature Review………………………………………………………...6
2.1 Evolution of the DVF……………………………………………………………...6
2.2 Relevant Literature on the Predictability under Different Models………………...8
2.3 Investigation of the DVF…………………………………………………………12
Chapter 3 Methodology…………………………………………………………….14
3.1 Conditional Volatility Measures………………………………………………….14
3.2 GARCH (1,1) process……………………………………………………………15
3.3 The One-Factor Stochastic Volatility model……………………………………..18
3.4 Datasets…………………………………………………………………………..21
Chapter 4 Empirical Results……………………………………………………….23
4.1 Implied Volatility Estimates……………………………………………………...23
4.2 Time Series Model Estimates…………………………………………………….24
4.3 Realized Index Volatilities………………………………………………………..25
4.4 A Comparison of the Selected Models…………………………………………...26
Chapter 5 Conclusion and Suggestion……………………………………………..28
Appendix…………………………………………………………………………….48
Reference…………………………………………………………………………….51
Table 1  Parameters of Least Squares Regression…………………………………..30
Table 2  Standard Deviations Implied in S&P 500 Call Prices
-Based on the 1-FSV Model……………………………………………….34
Table 3  Volatilities Estimated from GARCH (1,1) model…………………………35
Table 4  Realized Volatilities Calculated from S&P 500 Index…………………….36
Table 5  Realized Volatility Forecasts Errors……………………………………….37
Figure 1  Volatility Surface observed on 03 / 23 / 2004…………………………….38
Figure 2  Volatility Surface observed on 03 / 31 / 2004…………………………….39
Figure 3  Volatility Surface observed on 04 / 09 / 2004…………………………….40
Figure 4  Volatility Surface observed on 04 / 15 / 2004…………………………….41
Figure 5  Volatility Surface observed on 04 / 22 / 2004…………………………….42
Figure 6  Volatility Surface observed on 04 / 30 / 2004…………………………….43
Figure 7  Volatility Surface observed on 05 / 05 / 2004…………………………….44
Figure 8  Volatility Surface observed on 05 / 14 / 2004…………………………….45
Figure 9  Volatility Surface observed on 05 / 25 / 2004…………………………….46
Figure 10  Volatility Surface observed on 06 / 01 / 2004…………………………...47






                                    

Akgiray, V., 1989, “Conditional Heteroscedasticity in time series of stock returns：evidence and forecasts.” Journal of Business, 62, pp.55-80.

Andersen, T.G., T., Bollerslev, F.X., Diebold, and H., Ebens, 2000, “The distribution of realized stock return volatility.” Journal of Financial Economics, 61, pp.43-76.

Baillie, R.T., and T. Bollerslev, 1989, “The message in daily exchange rates：a conditional-variance tale.” Journal of Business and Economic Statistics, 7,pp.297-305.

Baillie, R.T., and R.P. DeGennaro, 1990, “Stock returns and volatility.” Journal of Financial and Quantitative Analysis, 25, pp.203-214.

Bevan J. Blair, Ser-Huang Poon and Stephen J. Taylor, 2001, “Forecasting S&P 100 Volatility：The Incremental Information Content of Implied Volatilities and High-Frequency Index Returns.” Journal of Econometrics, 105, pp.5-26.

Black, F., and M., Scholes, 1973, “The Pricing of options and Corporate liabilities.” Journal of political Economy, 81, pp.637-659.

Bollerslev, T., 1986, “Generalized autoregressive conditional heteroscedasticity.” Journal of Econometrics, 31, pp.307-327.

Bollerslev, T., R.Y. Chou and K.F. Kroner, 1992, “ARCH modeling in finance：a review of the theory and empirical evidence.” Journal of Econometrics, 52, pp.5-59.

Buraschi, Andrea, and Jens C., Jackwerth, 1998, “Explaining option prices：Deterministic vs. stochastic models.” Working paper, London Business School.

Campbell, T.Y., and L. Hentschel, 1992, “No News is Good News：An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics, Vol 31, No.3, pp.281-318.

Canina, L., and S. Figlewski, 1993, “The Informational Content of Implied Volatility.” Review of Financial Studies, 6, pp.659-681.

Christensen, B. J., and Prabhala, N.R., 1998, “The relationship between implied and realized volatility.” Journal of Financial Economics, 50, pp.125-150.

Coulson, N.E., and R.P., Robins, 1985, “Aggregate Economic Activity and the Variance of Inflation：Another Look.” Economic Letters, 17, pp.71-75.

Cox, J.C., and S.A., Ross, 1976, “The Valuation of Options for Alternative Stochastic processes.” Journal of Financial Economics, 3, pp.145-166.

Cox, J.C., S.A., Ross, and M., Rubinstein, 1979, “Option Pricing：A Simplified Approach.” Journal of Financial Economics, 7, pp.229-263.

Day, T.E., and C.M., Lewis, 1988, “The behavior of the volatility implicit in the prices of stock index options.’ Journal of Financial Economics, 22, pp.103-122.

Day, T. E., and C.M., Lewis, 1992, “Stock market volatility and information content of stock index options.” Journal of Econometrics, 52, pp.267-287.

Day, T. E., and C.M., Lewis, 1993, “Forecasting Futures Market Volatility.” Journal of Derivatives, pp.33-50.

Derman, Emanuel, and Iraj Kani, 1994, “Riding on a Smile.” Risk, Volume 7, No.2, pp.32-39.

Dumas, Bernard, Jeff Fleming, and Robert E. Whaley, 1998, “Implied Volatility Functions：Empirical Tests.” Journal of Finance, 53, pp.2059-2106.

Dupire, Bruno, 1994, “Pricing with a smile.” Risk, 7, pp.18-20.

Ebens, H., 1999, “Realized stock index volatility.” Working paper, No.420, Department of Economics, Johns Hopkins University.

Engle, R.F., 1982, “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.” Econometrica, 50, pp.987-1008.

Engle, R.F., D.M., Lilien, and R.P. Robins, 1987, “Estimating the Time Varying Risk Premia in the Term Structure：The ARCH-M Model.” Econometrica, 55, pp.391-407.

Fleming, J., 1998, “The quality of market volatility forecasts implied by S&P 100 index option prices.” Journal of Empirical finance, 5, pp.317-345.

Franks, Julian R., and Eduardo S. Schwartz. 1988, “The stochastic behavior of market variance implied in the prices of index options：Evidence on leverage, volume, and other effects.” Unpublished manuscript (university of California at Los Angeles, Los Angeles, CA).

French, Kenneth R., G. William Schwert, and Robert F. Stambaugh, 1987, “Expected stock returns and volatility.” Journal of Financial Economics, 8, pp.55-70.

Harvey, Campbell R., 1991 “The specification of conditional expectations.’ Unpublished manuscript (Duke University, Durham, NC).

Harvey, C.R., and R.E., Whaley, 1992a, “Market volatility prediction and the efficiency of the S&P 100 index option market.” Journal of Financial Economics, 31, pp.43-73.

Harvey, C.R., and R.E., Whaley, 1992b, “Dividends and S&P 100 index options.” Journal of Futures Markets, 12, pp.123-137.

Heynen, R., A.G.Z. Kemna, and T. Vorst, 1994, “Analysis of the Term Structure of Implied Volatilities.” Journal of Financial and Quantitative Analysis, 29, pp31-56.

Heston, S.L., and S. Nandi, 2000, “A Closed-Form GARCH Option Valuation Model.” The Review of Financial Studies, Vol.13, No.3, pp.585-625.

Hsieh, D.A., 1989, “Modelling heteroscedasticity in daily foreign-exchange rates.” Journal of Business and Economic Statistics, 7, pp.307-317.

Hull, J., and A. White, 1987, “The Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance 42, No.2, pp.281-300.

Jorion, P., 1995, “Predicting volatility in the foreign exchange market.” Journal of Finance, 50, pp.507-528.

Kreisler, M., 1998, “Information behind the implied volatility smile：empirical
results.” Ph.D. dissertation, University of Pennsylvania.

Lamoureux, D., and W. Lastrapes, 1993, “Forecasting Stock-Return Variance：Toward an Understanding of Stochastic Implied Volatilities.” Review of Financial Studies, 6, pp.293-326.

Latane, H.A., and R.J., Rendleman, 1976, “Standard Deviations of Stock Price Ratios Implied in Option Prices.” Journal of Finance,31, pp.369-381.

Mark, Britten-Jones, and Anthony Neuberger, 2000, “Option Prices, Implied Price Process, and Stochastic Volatility.” Journal of Finance, Vol.55, No.2, pp.839-866.

Merton, R.C., 1973a, “An Intertemporal Capital Asset Pricing Model.” Econometrica, Vol.41, No.5, pp.867-887.

Merton, R.C., 1976, “Option Pricing When Underlying Stock Returns Are Discontinuous.” Journal of Financial Economics, 3, pp.125-144.

Merville, Larry J., and Dan R., Pieptea, 1988, “Stock price volatility, mean-reverting diffusion and noise.” Journal of Financial Economics, 24, pp.193-214.

Noh, J., Engle, R.F., and Kane A., 1994, “Forecasting Volatility and option Prices of the S&P 500 Index.’ Journal of Derivatives, 1, pp.17-30.

Officer, Robert R., 1973, “The variability of the market factor of the NYSE.” Journal of Business, 46, pp.434-453.

Pagan, Adrian R. and G. Willian Schwert, 1990, “Alternative models for conditional stock volatility.” Journal of Econometrics, 45, pp.267-290.

Park, H.Y., and R.S., Sears, 1985, “Estimating Stock Index Futures Volatility through the Prices of their options.” Journal of Futures Market, Vol.9, No.4, pp.223-237

Pindyck, R. S., 1984, “Risk, Inflation, and the stock market.” American Economic Review, 74, pp.335-351.

Poterba, J., and l. Summers, 1986, “The Persistence of Volatility and Stock Market Fluctuations.” American Economic Review, 76, pp.1141-1151.

Rubinstein, Mark, 1994, “Implied Binomial Trees.” Journal of Finance, 49, pp.771-818.

Schmalensee, R., and R.R. Trippi, 1978, “Common Stock Volatility Expectation Implied by Option Prices.” Journal of Finance, 33, pp.129-147.

Schwert, G. William, 1990, “Stock volatility and the crash of ’87.” Review of Financial Studies, 3, pp.77-101.

Shimko, David, 1993, “Bounds of probability.” Risk, 7, pp.33-37.

Tsay, R. 1987,”Conditional heteroscedastic time series models.” Journal of the American Statistical Association, 82, pp.590-604

Wang, T.S., and Y, S.Y., 2005, “One-Factor Stochastic Volatility Implied by Current Options. Unpublished manuscript, (National University of Kaohsiung, and National Chung Hsing University)

Wiggins, James B., 1987, “Option values under stochastic volatility：Theory and empirical estimates.” Journal of Financial Economics, 19, pp.351-372.

Xu, X., and Taylor, S. J., 1995, “Conditional volatility and the informational efficiency of the PHLX currency options market.” Journal of Banking and Finance, 19, pp.803-821.

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校外：2005-10-19公開

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