TY - JOUR
T1 - Closed-form variance swap prices under general affine GARCH models and their continuous-time limits
AU - Badescu, Alexandru
AU - Cui, Zhenyu
AU - Ortega, Juan Pablo
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
KW - Affine GARCH models
KW - Diffusion limits
KW - Realized variance
KW - Variance dependent pricing kernels
KW - Variance swaps
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U2 - 10.1007/s10479-018-2941-9
DO - 10.1007/s10479-018-2941-9
M3 - Article
AN - SCOPUS:85049028561
SN - 0254-5330
VL - 282
SP - 27
EP - 57
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1-2
ER -