Economics at your fingertips  

Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics

Shunwei Zhu () and Bo Wang ()
Additional contact information
Shunwei Zhu: University of Shanghai for Science and Technology
Bo Wang: University of Shanghai for Science and Technology

Computational Economics, 2019, vol. 53, issue 4, 1421-1442

Abstract: Abstract Being able to generate a volatility smile and adequately explain how it moves up and down in response to changes in risk, stochastic volatility models have replaced BS model. A single-factor volatility model can generate steep smiles or flat smiles at a given volatility level, but it cannot generate both for given parameters. In order to match the market implied volatility surface precisely, Grasselli introduced a 4/2 stochastic volatility model that includes the Heston model and the 3/2 model, performing as affine and non-affine model respectively. The present paper is intended to further investigate the 4/2 model, which falls into four parts. First, we apply Lewis’s fundamental transform approach instead of Grasselli’s method to deduce PDEs, which is intuitional and simple; Then, we use a result derived by Craddock and Lennox using Lie Symmetries theory for PDEs, and the results are more objective and reasonable; Finally, through adopting the data on S&P 500, we estimate the parameters of the 4/2 model; Furthermore, we investigate the 4/2 model along with the Heston model and the 3/2 model and compare their different performances. Our results illustrate that the 4/2 model outperforms the Heston and the 3/2 model for the fitting problem.

Keywords: Stochastic volatility; Fundamental transform; 4/2 model; Lie’s symmetries; Laplace transform (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2019-11-06
Handle: RePEc:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9815-8