TY - JOUR
T1 - Variance swaps valuation under non-affine GARCH models and their diffusion limits
AU - Badescu, Alexandru
AU - Chen, Yuyu
AU - Couch, Matthew
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based discretely sampled variance swaps. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as the pricing kernel candidate. Following standard assumptions on time-varying GARCH parameters, we show that these quantities converge respectively to fair strikes of discretely and continuously sampled variance swaps that are constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we further investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns.
AB - In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based discretely sampled variance swaps. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as the pricing kernel candidate. Following standard assumptions on time-varying GARCH parameters, we show that these quantities converge respectively to fair strikes of discretely and continuously sampled variance swaps that are constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we further investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns.
KW - CBOE VIX
KW - Diffusion limits
KW - Extended Girsanov principle
KW - Non-Gaussian GARCH models
KW - Variance swaps
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U2 - 10.1080/14697688.2018.1478120
DO - 10.1080/14697688.2018.1478120
M3 - Article
AN - SCOPUS:85052055473
SN - 1469-7688
VL - 19
SP - 227
EP - 246
JO - Quantitative Finance
JF - Quantitative Finance
IS - 2
ER -