Abstract
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.
Highlights
In previous work, Bajo et al [1] investigated the optimal options hedging strategy for a firm, where the role of production risk and basis risk were taken into account
We extend the previous research by allowing the simultaneous hedging choice of futures and options
We show a potentially important role of futures when there are price risks be it additive or multiplicative background risk
Summary
Bajo et al [1] investigated the optimal options hedging strategy for a firm, where the role of production risk and basis risk were taken into account. Wong [26] examined the production and futures hedging decisions of a competitive firm under output price uncertainty and with state-dependent background risk. Background risk is generally correlated with price risk Based on these considerations, this paper takes into account both correlated additive and multiplicative risk into the hedging model, and discusses how the background risk affects the optimal decisions. We study how an investor can optimally choose an options contract and futures position to minimize the risk exposure It needs to introduce the risk measures. 2. We present a general model wherein many existing pieces of research are its special conditions by considering different additive and multiplicative background risks. We give some results for the general utility function when the investor faces correlated price risk and background risk with futures and options for hedging.
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