嵌入收益保证股票挂钩票据的最优投资策略

摘要

本文从投资机构的视角出发,将发行嵌入收益保证的股票挂钩票据(GELN)的最优投资策略问题转换为收益保证下的最优投资策略问题进行研究.在随机利率框架下,利用随机最优控制的方法得到了最优投资策略的解.结论表明最优投资策略可以分为三部分:投机策略、利率对冲策略、收益保证对冲策略.由于在GELN产品的标准收益结构中设定了收益的上下限,这就相当于投资机构卖出了一个牛市价差期权给投资者,期权价值被反映在最优化问题的目标函数中,所以最优投资策略解中出现了新的期权参数项.%A competitive investment institution is capable of helping investors ensure maximization of their return on investment (ROI) in equity-linked notes. This study proposes an optimal investment strategy for guaranteed equity-linked notes fiom the perspective of investment institutions. The current literature studies optimal investment strategy based on the assumption of simple returns with low limits. However, this assumption is not sufficient to understand the investment strategy for guaranteed equity-linked notes.This paper adopts a class of standard profit structures of guaranteed equity-linked notes as a reference standard to derive both lower and upper return guarantees limits. A guarantee of ROI can further complicate the process of formulating an optimal investment strategy. This paper solves optimal investment problems associated with new forms of return guarantees by introducing the bull spreads option. The stochastic optimal control method is adopted to improve the existing investment portfolio theory.The result indicates that optimal investment strategies should include three parts: speculative portfolio strategy, hedge strategy for stochastic interest rates, and hedge strategy for a ROI guarantee. The investment portfolio can affect the option price of an asset,thereby affecting the first order derivative of option price and interest rate in hedge strategies for ROI guarantee and stochastic interest rates.The investment strategy is adjusted dynamically through option items in onder to ensure that investment strategy is optimal. Our rasuh shows that the optimal wealth of our proposed investment strategy is always higher than the guaranteed ROI. In conclusion, the proposed investment strategy ensures that investors can at least have a guaranteed ROI.