Diversification with options and structured products

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.