Study of Implied Volatility Through Principal Component Analysis
Abstract
The effect of a large number of variables over a range becomes difficult to differentiate financial effects produced by different variables correlated source. By the method of principal components (PCA) technique and the eigenvectors and eigenvalues is transformed to an orthonormal basis in a few variables explaining the main effects. This idea is applied to the implied volatility of the Mexican derivatives market getting two variables, level, trend and curvature of the main explanation.
Keywords
Volatility, PCA, eigenvalues, eigenvectors
References
- Alexander, C., "Principal Component Analysis of Implied Volatility Smiles and Skwes" ISMA Centre Discussion Papers in Finance 2000-10, University of Reading U.K.
- Derman, E. (1999), "Volatility Regimes". RISK Magazine 12:4 pp 55-59.
- Derman, E., and Kamal (1997), "The Patterns of Change in Implied Index Volatilities". Quantitative Strategies Research Notes, Goldman Sachs.
- Derman, E., and Kani (1994), "Riding on a Smile". RISK Magazine 7:2 pp 32-39.
- Flenger, M.; W. hardle, and C. Villa (2000), "The dynamics of Implied Volatilities. A common Principal Component Approach".
- Reiswish D., and M. Tompkins, "Potential PCA Interpretation Problems for Volatility Smile Dynamics. Centre for practical quantitative finance Frankfurt School of Finance and Management", Working Paper Series No.19.
- Resumen y Análisis del Mercado Mexicano de Derivados (Market Statistics) (Enero-Septiembre 2012).
- Skiadopoulos, G.; S. Hodges, and L. Clewlow (1998). "The Dynamics of Implied Volatility Surfaces". Financial Options Research Centre Preprint 1998/86 Warwick Business School, University of Warwick UK.