none

This dissertation consists of two chapters that examine the construction of financial market volatility indexes and their forecasting efficiency across predictive regression models. Each of the chapter is devoted to diferent volatility measures which are related and evaluated in thframework of forecasting regressions.

The first chapter studies the sampling and liquidity issues in constructing volatility indexes, VIX and VXO, in emerging options market like Taiwan. VXO and VIX have been widely used to measure the 22-day forward volatility of the market. However, for an emerging market, VXO and VIX are difficult to measure with accuracy when tradings of the second and next to second nearby options are illiquid. The chapter proposes four methods to sample the option prices across liquidity proxies – five different days of rollover rules – for option trades to construct volatility index series. The paper finds that, based on the sampling method of the average of all
midpoints of bid and ask quote option prices, the volatility indexes constructed by minute-tick data have less missing data and more efficient in volatility forecast than the method suggested by CBOE. Additionally, illiquidity in emerging options market does not, based on different rollover rules, lead to substantial biases in the forecasting effectiveness of the volatility indexes.Finally, the forecasting ability of VIX, in terms of naive forecasts and forecasting regressions, is superior to VXO in Taiwan.

The second chapter uses high-frequency intraday volatility as a benchmark to measure the efficacy of model-free and model-based econometric models. The realized volatility computed from intraday data has been widely regarded as a more accurate proxy for market volatility than squared daily returns. The chapter adopts several time series models to assess the fore-casting efficiency of future realized volatility in Taiwan stock market. The paper finds that, for 1-day directional accuracy forecast performance, semiparametric fractional autoregressive model (SEMIFAR, Beran and Ocker, 2001) ranks highest with 78.52% hit accuracy, followed
by multiplicative error model (MEM, Engle, 2002), and augmented GJR-GARCH model. For 1-day forecasting errors evaluated by root mean squared errors (RMSE), GJR-GARCH model augmented with high-low range volatility ranks highest, followed by SEMIFAR and MEM model, both of which, however, outperform augmented GJR-GARCH by the measure of mean absolute value (MAE) and p-statistics (Blair et al., 2001).

1 Do Liquidity and Sampling Matter in Volatility Indexes? Empirical Evidence
in Taiwan 1
1.1 Introduction 1
1.2 Data and Method Description 5
1.2.1 Data 5
1.2.2 Measures of Implied Volatility Index 6
1.3 Summary Statistics 8
1.3.1 Descriptive Statistics 8
1.3.2 Efficiency of Liquidity 8
1.4 Measurement of Forecasting Efficiency 9
1.4.1 Naive Volatility Forecasts 10
1.4.2 Volatility Forecast Regressions 11
1.5 Conclusion 12
1.6 Tables 14
2 The Efficacy of Model-Based Volatility Forecasting 21
2.1 Introduction 21
2.1.1 Realized Volatility 21
2.1.2 Range-Based Volatility 23
2.2 Model Specifications 25
2.2.1 RV-based Models 25
2.2.2 Return-based Models 26
2.3 Empirical Results 29
2.3.1 Forecasting Evaluations 29
2.4 Econometric Analysis 32
2.5 Conclusion 33
2.6 Tables 34
2.7 Figures 37

Alizadeh, S., M. W. Brandt, and F. X. Diebold. Range-based estimation of stochastic volatility
models. The Journal of Finance, 57:1047–1091, 2002.
Andersen, T. G. and T. Bollerslev. Intraday periodicity and volatility persistence in financial
markets. Journal of Empirical Finance, 4:115–158, 1997.
Andersen, T. G. and T. Bollerslev. DM-dollar volatility: intraday activity patterns, macroe-
conomic announcements, and longer-run dependencies. The Journal of Finance, 53:219–265,
1998.
Andersen, T. G., T. Bollerslev, F. X. Diebold, and H. Ebens. The distribution of stock return
volatility. Journal of Financial Economics, 61:43–76, 2001a.
Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys. The distribution of exchange rate
volatility. Journal of American Statistical Association, 96:42–55, 2001b.
Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys. Modeling and forecasting realized
volatility. Econometrica, 71:579–625, 2003.
Andersen, T. G. and O. Bondarenko. Construction and interpretation of model-free implied
volatility, 2007. National Bureau of Economic Research Working Paper 13449, Cambridge,
MA.
Andersen, T. G., P. Frederiksen, and A. D. Staal. The information content of realized volatility
forecasts, 2007. Working paper.
Baillie, R. T., T. Bollerslev, and H. O. Mikkelsen. Fractionally integrated generalized autore-
gressive conditional heteroskedasticity. Journal of Econometrics, 74:3–30, 1996.
Bandi, F. M. and B. Perron. Long memory and the relation between implied and realized
volatility. Journal of Financial Econometrics, 4(4):636–670, 2006.
Bandi, F. M. and J. R. Russell. Microstructure noise, realized volatility, and optimal sampling,
2005. Working paper, University of Chicago.
Barndorff-Nielsen, O. E. and N. Shephard. Econometric analysis of realized volatility and its use
in estimating stochastic volatility model. Journal of Royal Statistical Society B, 64:253–280,
2002.
Barndorff-Nielsen, O. E. and N. Shephard. Realized power variation and stochastic volatility.
Bernoulli, 9:243–265, 2003.
Barndorff-Nielsen, O. E. and N. Shephard. Power and bi-power variation with stochastic volatil-
ity and jumps (with discussion). Journal of Financial Econometrics, 2:1–48, 2004.
Barndorff-Nielsen, O. E. and N. Shephard. Econometrics for testing for jumps in financial
economics using bi-power variation. Journal of Financial Econometrics, 4:1–30, 2006.
Beckers, S. Standard deviations implied in option prices as predictors of future stock price
variability. Journal of Banking and Finance, 5(3):363–381, 1981.
Beran, J., Y. Feng, and D. Ocker. SEMIFAR models. Technical Report SFB 475, University
of Dortmund, 1999.
Beran, J. and D. Ocker. SEMIFAR forecasts, with applications to foreign exchange rates.
Journal of Statistical Planning and inference, 80:137–153, 1999.
Beran, J. and D. Ocker. Volatility of stock market indices - an analysis based on SEMIFAR
models. Journal of Business and Economic Statistics, 19:103–116, 2001.
Bilson, J. F. O. An assessment of alternative models of financial market volatility, volume
Handbook of Risk. New York: John Wiley & Sons, 2003.
Blair, B. J., S.-H. Poon, and S. J. Taylor. Forecasting S&P 100 volatility: The incremental
information content of implied volatilities and high-frequency index returns. Journal of
Econometrics, 105(1):5–26, 2001.
Bollen, B. and B. Inder. Estimating daily volatility in financial markets utilizing intraday data.
Journal of Empirical Finance, 9:551–562, 2002.
Bollerslev, T. and H. O. Mikkelsen. Modeling and pricing long memory in stock market volatil-
ity. Journal of Econometrics, 73:151–184, 1996.
Britten-Jones, M. and A. Neuberger. Option prices, implied price processes, and stochastic
volatility. The Journal of Finance, 55(2):839–866, 2000.
Canina, L. and S. Figlewski. The information content of implied volatility. Review of Financial
Studies, 6(3):659–681, 1993.
Carr, P. and D. Madan. Towards a Theory of Volatility Trading, chapter 29, pages 417–427.
Risk Books, 1998.
Carr, P. and L. Wu. Time-changed L′evy processes and option pricing. Journal of Financial
Economics, 71:113–141, 2004.
Chiras, D. P. and S. Manaster. The information content of option prices and a test of market
efficiency. Journal of Financial Economics, 6(2-3):659–681, 1978.
Chou, R. Y., H. Chou, and N. Liu. Range volatility models and their applications in finance,
2008. Working paper.
Christensen, B. J. and M. Ø. Nielsen. Asymptotic normality of narrow-band least squares in the
stationary fractional cointegration model and volatility forecasting. Journal of Econometrics,
133(1):343–371, 2006.
Christensen, B. J. and N. R. Prabhala. The relatioin between realized and implied volatility.
Journal of Financial Economics, 50(2):125–150, 1998.
Christensen, B. J. and C. Strunk-Hansen. New evidence on the implied-realized volatility
relation. European Journal of Finance, 8(2):187–205, 2002.
Corrado, C. J. and T. W. Miller. The forecast quality of CBOE implied volatility indexes.
Journal of Futures Markets, 25(4):339–373, 2005.
Dahl, C. M. and S. Hylleberg. Specifying nonlinear econometric models by flexible regression
models and relative forecast performance, 1999. Working paper, Department of Economics,
Unversity of Aarhus, Denmark.
Day, T. E. and C. M. Lewis. The behavior of the volatility implicit in the prices of stock index
options. Journal of Financial Economics, 22(1):103–122, 1988.
Demeterfi, K., E. Derman, M. Kamal, and J. Zou. A guide to volatility and variance swaps.
Journal of Derivatives, 6(2):9–32, 1999.
Dupire, B. Model art. Risk, pages 118–120, 1993.
Engle, R. New frontiers for ARCH models. Journal of Applied Econometrics, 17:425–446, 2002.
Engle, R. F. and G. M. Gallo. A multiple indicators model for volatility using intra-daily data.
Journal of Econometrics, 131:3–27, 2006.
Fleming, J. The quality of market volatility forecasts implied by S&P 100 index option implied
volatility. Journal of Empirical Finance, 5:317–345, 1998.
Fleming, J. The economic significance of the forecast bias of S&P 100 index option implied
volatility. Advances in Futures and Options Research, 10:219–251, 1999.
Garman, M. and M. Klass. On the estimation of security price volatilities from historical data.
Journal of Business, 53:67–78, 1980.
Glosten, L. R., R. Jagannathan, and D. E. Runkle. On the relation between the expected
value and the volatility of the normal excess return on stocks. The Journal of Finance,
48:1779–1801, 1993.
Hansen, P. R. and A. Lunde. An unbiased measure of realized variance, 2004. Working paper,
Stanford University.
Harvey, C. R. and R. E. Whaley. S&P 100 index option volatility. The Journal of Finance,
46(4):1551–1561, 1991.
Jiang, G. J. and Y. S. Tian. Gauging the ”investor fear gauge”: Implementation problems in
the CBOE’s new volatility index and a simple solution, 2005a. Working paper.
Jiang, G. J. and Y. S. Tian. The model-free implied volatility and its information content.
Review of Financial Studies, 18(4):1305–1342, 2005b.
Jorion, P. Predicting volatility in the foreign exchange market. The Journal of Finance,
50(2):507–528, 1995.
Kunitomo, N. Improving the parkinson method of estimating security price volatilities. Journal
of Business, 65:295–302, 1992.
Lamoureux, C. G. and W. D. Lastrapes. Forecasting stock-return variance: Understanding of
stochastic implied volatilities. The Review of Financial Studies, 6(2):293–326, 1993.
Lanne, M. A mixture multiplicative error model for realized volatility. Journal of Financial
Econometrics, 4(4):594–616, 2006.
Latane, H. A. and R. J. Rendleman. Standard deviations of stock price ratios implied in option
prices. The Journal of Finance, 31(2):369–381, 1976.
Lobato, I. N. and N. E. Savin. Real and spurious long-memory properties of stock-market data.
Journal of Business and Economic Statistics, 16(3):261–268, 1998.
Madan, D. B., P. P. Carr, and E. C. Chang. The variance-gamma process and option pricing.
European Finance Review, 2:79–105, 1998.
Martens, M. and J. Zein. Predicting financial volatility: high frequency time series forecasts
vis a vis implied volatility. Journal of Future Markets, 24(11):1005–1028, 2004.
McAleer, M. and M. C. Medeiros. Realized volatility: a review. Econometric Reviews, 27:10–45,
2008.
Merton, R. C. On estimating the expected return on the market: an exploratory investigation.
Journal of Financial Economics, 8:323–361, 1980.
Neuberger, A. The log contract: A new instrument to hedge volatility. Journal of Portfolio
Management, 20(2):74–80, 1994.
Parkinson, M. The extreme value method for estimating the variance of the rate of return.
Journal of Business, 53:61–65, 1980.
Poon, S.-H. A practical guide to forecasting financial volatility. John Wiley & Sons, 1 edition,
2005.
Poteshman, A. M. Forecasting future volatility from option prices, 2000. Working paper,
University of Illinois at Urbana-Champaign.
Ray, B. K. and R. S. Tsay. Long-range dependence in daily stock volatilities. Journal of
Business and Economic Statistics, 18:254–262, 2000.
Rogers, L. and S. Satchell. Estimating variance from high, low and closing prices. Annals of
Applied Probability, 1:504–512, 1991.
Shu, J. H. and J. E. Zhang. Testing range estimators of historical volatility. Journal of Futures
Markets, 26:297–313, 2006.
Yang, D. and Q. Zhang. Drift independent volatility estimation based on high, low, open and
close prices. Journal of Business, 73:477–491, 2000.
Zivot, E. and J. Wang. Modeling Financial Time Series with S-PLUS. Springer, 2 edition,
2006.
4