Variance swaps valuation under non-affine GARCH models and their diffusion limits

Alexandru Badescu, Yuyu Chen, Matthew Couch, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)227-246
Number of pages20
JournalQuantitative Finance
Volume19
Issue number2
DOIs
StatePublished - 1 Feb 2019

Keywords

  • CBOE VIX
  • Diffusion limits
  • Extended Girsanov principle
  • Non-Gaussian GARCH models
  • Variance swaps

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