A Markovian empirical model for the VIX index and the pricing of the corresponding derivatives

Ying-Li Wang, Cheng-Long Xu and Ping He

Papers from arXiv.org

Abstract: In this paper, we propose an empirical model for the VIX index. Our findings indicate that the VIX has a long-term empirical distribution. To model its dynamics, we utilize a continuous-time Markov process with a uniform distribution as its invariant distribution and a suitable function $h$. We determined that $h$ is the inverse function of the VIX data's empirical distribution. Additionally, we use the method of variables of separation to get the exact solution to the pricing problem for VIX futures and call options.

Date: 2023-09
New Economics Papers: this item is included in nep-ger
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