Extreme-strike asymptotics for general Gaussian stochastic volatility models

Archil Gulisashvili (), Frederi Viens () and Xin Zhang ()
Additional contact information
Archil Gulisashvili: Ohio University
Frederi Viens: Michigan State University
Xin Zhang: Purdue University

Annals of Finance, 2019, vol. 15, issue 1, No 3, 59-101

Abstract: Abstract We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen–Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or small values of the variable, and study the wing behavior of the implied volatility in these models. Our main result provides explicit expressions for the first three terms in the expansion of the implied volatility, based on three basic spectral-type statistics of the Gaussian process: the top eigenvalue of its covariance operator, the multiplicity of this eigenvalue, and the $$L^{2}$$ L 2 norm of the projection of the mean function on the top eigenspace. Numerical illustrations using the Stein–Stein and fractional Stein–Stein models are presented, including strategies for parameter calibration.

Keywords: Stochastic volatility; Implied volatility; Large strike; Karhunen–Loève expansion; Chi-squared variates; 60G15; 91G20; 40E05 (search for similar items in EconPapers)
JEL-codes: C6 G13 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Downloads: (external link)
http://link.springer.com/10.1007/s10436-018-0338-z Abstract (text/html)
Access to full text is restricted to subscribers.

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: https://EconPapers.repec.org/RePEc:kap:annfin:v:15:y:2019:i:1:d:10.1007_s10436-018-0338-z

Ordering information: This journal article can be ordered from
http://www.springer.com/finance/journal/10436/PS2

DOI: 10.1007/s10436-018-0338-z

Access Statistics for this article

Annals of Finance is currently edited by Anne Villamil

More articles in Annals of Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().