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Math. Comput. Appl. 2017, 22(1), 5; doi:10.3390/mca22010005

Optimal Hedging with Options and Futures against Price Risk and Background Risk

College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, China
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 21 October 2016 / Revised: 25 December 2016 / Accepted: 28 December 2016 / Published: 4 January 2017
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On the condition that both futures and options exist in the markets for hedging, this paper examines the optimal hedging strategy under price risk and background risk. Compared with the previous research, which has studied options hedging against basis risk and production risk being extended to options and futures hedging against price risk and background risk, we proposed a model and have taken the budget of buying options into consideration. The model is fairly general and some existing models are special cases of it. We firstly derive the necessary and sufficient conditions that guarantee the optimality of an under-hedge, a full-hedge and an over-hedge of futures for the risk-averse utility. Then, sufficient conditions are stipulated under which an over-hedge is optimal. Furthermore, we propose a program minimizing of tail conditional expectation (TCE), which is inherently equivalent to the risk measure of expected shortfall risk (ES) or the conditional VaR (CVaR) under the continuous-time framework. Finally, we find that ES, in our proposed model, is significantly smaller than the one in the model of options hedging only. Therefore, the results emphasize the need for combining futures hedging and options hedging, and it also shows that imposing background risk, whether it be additive or multiplicative, always has a great impact on the hedging efficiency. We also present some sensitivities of the relevant parameters to provide some suggestions for the investors. View Full-Text
Keywords: options hedging; futures hedging; background risk; expected shortfall; Monte Carlo simulation options hedging; futures hedging; background risk; expected shortfall; Monte Carlo simulation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Yu, X.; Sun, H. Optimal Hedging with Options and Futures against Price Risk and Background Risk. Math. Comput. Appl. 2017, 22, 5.

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