Consistent Modeling of VIX and Equity Derivatives Using a 3/2 Plus Jumps Model

Jan Baldeaux and Alexander Badran

No 306, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper quasi-closed-form solutions are derived for the price of equity and VIX derivatives under the assumption that the underlying follows a 3/2 process with jumps in the index. The newly-found formulae allow for an empirical analysis to be performed. In the case of the pure-diffusion 3/2 model, the dynamics are rich enough to capture the observed upward-sloping implied-volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the consistent modeling of equity and VIX derivatives. We find that the 3/2 plus jumps model is more parsimonious than competing models from its class; it is able to accurately capture the joint dynamics of equity and VIX derivatives, without sacrificing analytic tractability. The model produces a good short-term fit to the implied volatility of index options due to the richer dynamics, while retaining the analytic tractability of its pure-diffusion counterpart.

Keywords: stochastic volatility plus jumps model; 3/2 model; VIX derivatives (search for similar items in EconPapers)
JEL-codes: C6 C63 G1 G13 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2012-03-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published as: Baldeaux, J. and Badran, A., 2014, "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model", Applied Mathematical Finance, 21(4), 299-312.

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https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp306.pdf (application/pdf)

Related works:
Journal Article: Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model (2014)
Working Paper: Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model (2012)
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