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Performance of Tail Hedged Portfolio with Third Moment Variation Swap

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Abstract

The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the realized third moment variation are exchanged. The probability density function of the hedged portfolio with the third moment variation swap was examined using a partial differential equation approach. An alternating direction implicit method was used for numerical analysis of the partial differential equation. Under the stochastic volatility and jump diffusion stochastic volatility models, the distributions of the hedged portfolio return are symmetric and have more Gaussian-like thin-tails.

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Acknowledgments

Byoung Ki Seo was supported by the 2012 Research Fund (1.120071.01) of UNIST (Ulsan National Institute of Science and Technology). Kyungsub Lee was supported by the 2015 Yeungnam University Research Grant.

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Correspondence to Byoung Ki Seo.

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Lee, K., Seo, B.K. Performance of Tail Hedged Portfolio with Third Moment Variation Swap. Comput Econ 50, 447–471 (2017). https://doi.org/10.1007/s10614-016-9593-0

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