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Pricing VIX options with stochastic volatility and random jumps

Journal Article


Abstract


  • This study presents an analytical exact solution for the price of VIX

    options under stochastic volatility model with simultaneous jumps in the asset price

    and volatility processes. We shall demonstrate that our new pricing formula can be

    used to efficiently compute the numerical values of a VIX option. While we also

    show that the numerical results obtained from our formula consistently match those

    obtained from Monte Carlo simulation perfectly as a verification of the correctness

    of our formula, numerical evidence is offered to illustrate that the correctness of the

    formula proposed in Lin and Chang (J Futur Markets 29(6), 523–543, 2009) is in

    serious doubt.Moreover, some important and distinct properties of VIX options (e.g.,

    put-call parity, hedging ratios) are also examined and discussed.

Publication Date


  • 2013

Citation


  • Lian, G. & Zhu, S. (2013). Pricing VIX options with stochastic volatility and random jumps. Decisions in Economics and Finance: a journal of applied mathematics, 36 71-88.

Scopus Eid


  • 2-s2.0-84875526854

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1209

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 71

End Page


  • 88

Volume


  • 36

Place Of Publication


  • Netherlands

Abstract


  • This study presents an analytical exact solution for the price of VIX

    options under stochastic volatility model with simultaneous jumps in the asset price

    and volatility processes. We shall demonstrate that our new pricing formula can be

    used to efficiently compute the numerical values of a VIX option. While we also

    show that the numerical results obtained from our formula consistently match those

    obtained from Monte Carlo simulation perfectly as a verification of the correctness

    of our formula, numerical evidence is offered to illustrate that the correctness of the

    formula proposed in Lin and Chang (J Futur Markets 29(6), 523–543, 2009) is in

    serious doubt.Moreover, some important and distinct properties of VIX options (e.g.,

    put-call parity, hedging ratios) are also examined and discussed.

Publication Date


  • 2013

Citation


  • Lian, G. & Zhu, S. (2013). Pricing VIX options with stochastic volatility and random jumps. Decisions in Economics and Finance: a journal of applied mathematics, 36 71-88.

Scopus Eid


  • 2-s2.0-84875526854

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1209

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 71

End Page


  • 88

Volume


  • 36

Place Of Publication


  • Netherlands