Equity Volatility Smile and Skew under a CEV-based Structural Leverage Model

Authors

Min Chen, Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218, USA\\ Ohio National Financial Services, Cincinnati, Ohio 45242, USAFollow

Author Country (or Countries)

USA

Abstract

The leverage effect is widely considered to be the major contributor to volatility skew in the stock option market. This study concentrates on explicit modeling of corporate leverage. The asset-equity relation is modeled by a perpetual American option, and the asymmetry of the asset return distribution is addressed by introducing a Constant Elasticity of Variance (CEV) asset dynamic. The model retains closed-form representation of firm equity with respect to asset and liability. This provides a convenient simplification to equity option pricing, so that the model can be calibrated to stock prices and the entire volatility structure. This model demonstrates how the volatility smile, as well as skew, can be accommodated by the structural model, and also successfully explains why low-leverage stocks could still have a non-trivial volatility structure. A cross-sectional study shows that the calibrated parameters effectively outline the financial characteristics of the leveraged firms. The credit quality measure generated from this model is also more informative in terms of explaining Credit Default Swap (CDS) spread movements.

Recommended Citation

Chen, Min (2015) "Equity Volatility Smile and Skew under a CEV-based Structural Leverage Model," Applied Mathematics & Information Sciences: Vol. 09: Iss. 3, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/1