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Closed-form variance swap prices under general affine GARCH models and their continuous-time limits.

Closed-form variance swap prices under general affine GARCH models and their continuous-time limits.

Authors :
Badescu, Alexandru
Cui, Zhenyu
Ortega, Juan-Pablo
Source :
Annals of Operations Research. Nov2019, Vol. 282 Issue 1/2, p27-57. 31p.
Publication Year :
2019

Abstract

Fully explicit closed-form expressions are developed for the fair strike prices of discrete-time variance swaps under general affine GARCH type models that have been risk-neutralized with a family of variance dependent pricing kernels. The methodology relies on solving differential recursions for the coefficients of the joint cumulant generating function of the log price and the conditional variance processes. An alternative derivation is provided in the case of Gaussian innovations. Using standard assumptions on the asymptotic behavior of the GARCH parameters as the sampling frequency increases, the diffusion limit of a Gaussian GARCH model is derived and the convergence of the variance swap prices to its continuous-time limit is further investigated. Numerical examples on the term structure of the variance swap rates and on the convergence results are also presented. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02545330
Volume :
282
Issue :
1/2
Database :
Academic Search Index
Journal :
Annals of Operations Research
Publication Type :
Academic Journal
Accession number :
139163167
Full Text :
https://doi.org/10.1007/s10479-018-2941-9