Minimizing CVaR in global dynamic hedging with transaction costs

Abstract

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.

Keywords:

• Hedging
• Risk measures
• Tail value-at-risk
• Conditional value-at-risk
• Dynamic programming
• Transaction costs

JEL Classifications:

• G32
• C61

Acknowledgements

The author would like to thank Geneviève Gauthier and the two anonymous referees for their helpful feedback. Financial support from Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada [BESC D3].