Different from diversification of stocks, there are two strategies to diversify portfolios consisting of options: one is to combine options on single underlying stocks, and the other one is to buy an option based on the index of these stocks. In this paper we analyse which diversification strategy is optimal for classical rational investors with constant relative risk aversion. We employ the Black–Scholes model and the stochastic volatility model of Heston for generating the processes of underlying stocks as well as pricing the derivatives. The results are developed first for options and then extended to some important classes of structured financial products: capital protected notes, discount certificates and bonus certificates. We find that investors’ choices on the two diversification strategies differ noticeably, but in general for convex payoffs index options are preferable, whereas for concave payoffs a portfolio of single stock options has usually higher utility.

与股票多样化不同，有两种由期权组成的使投资组合多样化的策略：一种是将单个基础股票的期权组合在一起，另一种是根据这些股票的指数购买期权。在本文中，我们分析了对于具有相对风险规避不变的经典理性投资者而言，哪种分散策略是最佳的。我们采用Heston的Black-Scholes模型和随机波动率模型来生成基础股票的过程以及对衍生产品进行定价。首先为期权开发结果，然后扩展到结构化金融产品的一些重要类别：资本保护票据，折扣证书和红利证书。我们发现，投资者在两种多元化策略上的选择存在明显差异，