The Analysis of Implied Volatilities
The analysis of volatility in financial markets has become a first rank issue in modern financial theory and practice: Whether in risk management, portfolio hedging, or option pricing, we need to have a precise notion of the market’s expectation of volatility. Much research has been done on the analysis of realized historic volatilities, Roll (1977) and references therein. However, since it seems unsettling to draw conclusions from past to expected market behavior, the focus shifted to implied volatilities, Dumas, Fleming and Whaley (1998). To derive implied volatiUties the Black and Scholes (BS) formula is solved for the constant volatility parameter σ using observed option prices. This is a more natural approach as the option value is decisively determined by the market’s assessment of current and future volatility. Hence implied volatility may be used as an indicator for market expectations over the remaining lifetime of the option.
- Aït-Sahalia, Y. and Lo, A. W. (1998). Nonparametric Estimation of State-Price Densities Implicit in Financial Assets, Journal of Finance Vol. LIII, 2, pp. 499–547. CrossRef
- Aït-Sahalia, Y. and Lo, A. W. (2000). Nonparametric Risk management and implied risk aversion, Journal of Econometrics 94, pp. 9–51. CrossRef
- Dumas, B., Fleming, J. and Whaley, R. E. (1998). Implied Volatility Functions: Empirical Tests, Journal of Finance Vol. LIII, 6, pp. 2059–2106. CrossRef
- Fengler, M. R., Härdle, W. and Villa, Chr. (2001). The Dynamics of Implied Volatilities: A Common Principal Components Approach, SfB 373 Discussion Paper No. 2001/38, HU Berlin.
- Flury, B. (1988). Common Principle Components Analysis and Related Multivariate Models, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York.
- Flury, B. and Gautschi, W. (1986). An Algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form SIAM Journal on Scientific and Statistical Computing, 7, pp. 169–184. CrossRef
- Härdle, W. (1990). Applied Nonparametric Regression, Econometric Society Monographs 19, Cambridge University Press. CrossRef
- Härdle, W., Müller, M., Sperlich, S. and Werwartz, A. (2002). Non- and Semiparametric Modelling, Springer, e-book http://www.xplore-stat.de
- Härdle, W. and Schmidt, P. (2002). Common Factors Governing VDAX Movements and the Maximum Loss, Financio/ Markets and Portfolio Management, forthcoming.
- Hafner, R. and Wallmeier, M. (2001). The Dynamics of DAX Implied Volatilities, International Quarterly Journal of Finance,, 1, pp. 1–27.
- Muirhead, R. J. (1982). Aspects of Multivariate Statistics, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York.
- Redelberger, T. (1994). Grundlagen und Konstruktion des VDAX-Volatilitatsindex der Deutsche Börse AG, Deutsche Börse AG, Frankfurt am Main.
- Roll, R. (1977). A Critique of the Asset Pricing Theory’s Tests: Part I, Journal of Financial Economics, 4, pp. 129–176. CrossRef
- Taleb, N. (1997). Dynamic Hedging: Managing Vanilla and Exotic Options, John Wiley & Sons, New York.
- Villa, C. and Sylla, A. (2000). Measuring implied surface risk using PCA in Franke, J., Härdle, W. and Stahl, G.: Measuring Risk in Complex Stochastic Systems, LNS 147, Springer Verlag, New York, pp. 131–147.
- The Analysis of Implied Volatilities
- Book Title
- Applied Quantitative Finance
- Book Subtitle
- Theory and Computational Tools
- Book Part
- Part III
- pp 127-144
- Print ISBN
- Online ISBN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
To view the rest of this content please follow the download PDF link above.