Modeling VIX Index Based on Semi-parametric Markov Models with Frank Copula

Andrejs Matvejevs, Jegors Fjodorovs


The research studies the estimation of a semi- parametric stationary Markov models based on a Frank copula density function. Described techniques allow us to estimate the parameters of the Frank copula, which has a better fit compared to previously selected regression models (estimators of the marginal distribution and the copula parameters are provided). We show how to apply our technique to the financial index VIX – a market mechanism that measures the 30-day forward implied volatility of the underlying index, the S&P500. Moreover, using MatLab we made VIX option index study – found the best copula fit under our condition, estimated nonlinear parameters and showed evaluation steps for copula based semi-parametric models.


Diffusion processes; Frank copula; Markov models; semi parametric regressions; VIX index

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