VIX Computation Based on Affine Stochastic Volatility Models in Discrete Time

Forthcoming on "Recent Advances in Commodity and Financial Modeling" Springer's International Series in Operations Research and Management Science.

16 Pages Posted: 29 Mar 2013 Last revised: 19 Dec 2015

See all articles by Asmerilda Hitaj

Asmerilda Hitaj

Università degli Studi di Milano-Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Lorenzo Mercuri

University of Milan

Edit Rroji

Polytechnic University of Milan - Department of Mathematics

Date Written: December 18, 2015

Abstract

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.

Keywords: Affine Stochastic Volatility, VIX, Implied Volatility Surface

JEL Classification: G13, C32

Suggested Citation

Hitaj, Asmerilda and Mercuri, Lorenzo and Rroji, Edit, VIX Computation Based on Affine Stochastic Volatility Models in Discrete Time (December 18, 2015). Forthcoming on "Recent Advances in Commodity and Financial Modeling" Springer's International Series in Operations Research and Management Science.. Available at SSRN: https://ssrn.com/abstract=2240562 or http://dx.doi.org/10.2139/ssrn.2240562

Asmerilda Hitaj

Università degli Studi di Milano-Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, 20126
Italy

Lorenzo Mercuri (Contact Author)

University of Milan ( email )

Via Festa del Perdono, 7
Milan, 20122
Italy

Edit Rroji

Polytechnic University of Milan - Department of Mathematics ( email )

Via Bonardi, 9
Milano, MI 20133
Italy

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