This paper proposed the optimal portfolio model maximizing returns and minimizing the risk expressed as CvaR under the assumption that the portfolio yield subject to heavy tail. We use fuzzy mathematics method to solve the multi-objectives model, and compare the model results to the case under the normal distribution yield assumption based on the portfolio VAR through empirical research. It is showed that our return is approximate to M-V model but risk is higher than M-V model. So it is illustrated that CVaR predicts the potential risk of the portfolio, which will help investors to cautious investment
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.
On March 26, 2018, Chinese crude oil futures start online trading in Shanghai futures exchange, a subsidiary of Shanghai international energy trading center. Chinese crude oil futures are expected to balance the current benchmark prices of WTI and brent .This study aims at analyzing the Chinese high frequency crude oil price. In this study, GARHC-type models are used namely GARCH and TARCH for modelling the high frequency Chinese crude oil yield. It is concluded that the TARCH model performs well as compared to GARCH models. At last, the VaR of the crude oil yield in the next day is calculated for comparative analysis.
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