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On the convexity correction approximation in pricing volatility swaps and VIX futures

Journal Article


Abstract


  • © World Scientific Publishing Company. Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second- order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

Publication Date


  • 2018

Citation


  • Zhu, S. & Lian, G. (2018). On the convexity correction approximation in pricing volatility swaps and VIX futures. New Mathematics and Natural Computation, 14 (3), 383-401.

Scopus Eid


  • 2-s2.0-85052241060

Number Of Pages


  • 18

Start Page


  • 383

End Page


  • 401

Volume


  • 14

Issue


  • 3

Abstract


  • © World Scientific Publishing Company. Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second- order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

Publication Date


  • 2018

Citation


  • Zhu, S. & Lian, G. (2018). On the convexity correction approximation in pricing volatility swaps and VIX futures. New Mathematics and Natural Computation, 14 (3), 383-401.

Scopus Eid


  • 2-s2.0-85052241060

Number Of Pages


  • 18

Start Page


  • 383

End Page


  • 401

Volume


  • 14

Issue


  • 3