||Options contain many investor’s future views toward future, thus many scholars estimate the volatility in Black-Scholes model by using option data. In this thesis, we provide a method to estimate volatility under Black-Scholes model. In our method, we consider a generalized linear regression to estimate the volatility under the Black-Scholes model by using all options. Afterwards, we use the estimated volatility to calculate Greeks and do dynamic hedging for TAIEX options at different strike price. The empirical results show that hedging using this method outperforms other benchmark methods, i.e., using|
implied volatilities or using standard deviations of historical log returns.
||Bakshi, G., N. Kapadia, and D. Madan (2003). Stock return characteristics, skew laws,|
and the differential pricing of individual equity options. Review of Financial Studies 16,
Bali, T. and A. Hovakimian (2009). Volatility spreads and expected stock returns. Management
Science 55, 1797–1812.
Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial
Economics 2, 95–121.
Black, F. and M. Scholes (1973). The pricing of options and corporate liabilities. The
Journal of Political Economy 81(3), 637–654.
Bollerslev, T., M. Gibson, and H. Zhou (2004). Dynamic estimation of volatility risk
premia and investor risk aversion from option-implied and realized volatilities. Finance
and Economics Discussion Series.
Brenner, M. and M. Subrahmanyam (1988). A simple solution to compute the implied
standard deviation. Financial Analysts Journal, 80–83.
Carr, P. and L. Wu (2009). Variance risk premiums. Review of Financial Studies 22,
Corrado, C. and T. Miller (1996). A note on a simple, accurate formula to compute
implied standard deviations. Journal of Banking and Finance 20, 595–603.
DeMiguel, V., Y. Plyakha, R. Uppal, and G. Vilkov (2013). Improving portfolio selection
using option-implied volatility and skewness. Journal of Financial and Quantitative
Analysis 48, 1813–1845.
Feinstein, S. (1988). A source of unbiased implied volatility forecasts. Working paper 88-9
, Federal Reserve Bank of Atlanta, 595–603.
Hanly, J. and J. Cotter (2005). Re-evaluating hedging performance. Journal of Futures
Markets 26(7), 677–702.
Haug, E. and J. Haug (1996). Implied forward volatility. Paper presented at the Third
Nordic Symposium on Contingent Claims Analysis in Finance 20, 595–603.
Haug, E. G. (2007). The Complete Guide to Option Pricing Formulas. New York:
Hull, J. C. (2011). Options, Futures, and Other Derivatives 8th. New Jersey: Prentice
Liu, Y. and Y. Wang (2013). Volatility estimation by combining stock price data and
option data. Statistics and Its Interface 6(4), 427–433.
Macmillan, L. G. (1993). Options as a Strategic Investment. New Jersey: Prentice Hall.
Madan, D. B. and P. P. Carr (1998). The variance gamma process and option pricing.
European Finance Review 2, 79–105.
Merton, R. C. (1976). Option pricing when underlting stock return are discontinuous.
Journal of Financial Economics 3, 125–144.
Roy, A. (1952). Safety first and the holding of assets. Econometrica 20(3), 431–449.