The Dynamics of Smiles

FORC series Pre-Prints: 98/85

Posted: 7 May 1998

See all articles by George S. Skiadopoulos

George S. Skiadopoulos

Queen Mary, University of London, School of Economics and Finance; University of Piraeus

Stewart D. Hodges

University of Warwick - Financial Options Research Centre (FORC)

Les Clewlow

Lacima; University of Warwick - Financial Options Research Centre (FORC); University of Technology Sydney (UTS) - School of Finance and Economics

Date Written: March 1998

Abstract

This empirical study is motivated by the models of Dupire (1992) and Derman and Kani (1997). We investigate the number and shape of shocks that move implied volatility smiles and subsequently we look at the correlation of changes in volatility with changes in the underlying asset. We achieve this by applying Principal Components Analysis on the changes in implied volatilities over time, for fixed ranges of days to maturity and in two different metrics: the strike and the moneyness metric. In contrast to earlier papers in the interest rate literature, we decide on how many principal components explain the implied volatilities dynamics, not by using rules of thumb, but by using Velicer's non-parametric criterion. Subsequently we use a ''Procrustes'' type rotation in order to interpret the retained components. The retained rotated principal components are used for the calculation of the correlation coefficients. We find similar results in both metrics regarding the number and shape of shocks. Two principal components explain the dynamics of smiles. After the rotation the first one is interpreted as shift and the second one has a Z-shape. The correlations for the first principal component depend metric, while for the second are positive under both metrics.

JEL Classification: G13

Suggested Citation

Skiadopoulos, George and Hodges, Stewart D. and Clewlow, Les, The Dynamics of Smiles (March 1998). FORC series Pre-Prints: 98/85, Available at SSRN: https://ssrn.com/abstract=82408

George Skiadopoulos (Contact Author)

Queen Mary, University of London, School of Economics and Finance

Lincoln's Inn Fields
Mile End Rd.
London, E1 4NS
United Kingdom

University of Piraeus ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

HOME PAGE: http://web.xrh.unipi.gr/faculty/gskiadopoulos/

Stewart D. Hodges

University of Warwick - Financial Options Research Centre (FORC) ( email )

Warwick Business School
Coventry CV4 7AL
United Kingdom
01203-523606 (Phone)

Les Clewlow

Lacima ( email )

London
United Kingdom

HOME PAGE: http://www.lacimagroup.com

University of Warwick - Financial Options Research Centre (FORC)

Coventry CV4 7AL
United Kingdom

HOME PAGE: http://www.wbs.ac.uk/expertise/research_teaching/f

University of Technology Sydney (UTS) - School of Finance and Economics ( email )

Haymarket
Sydney, NSW 2007
Australia

HOME PAGE: http://www.business.uts.edu.au/finance/

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