Improving the Design of Financial Products in a Multidimensional Black-Scholes Market

Abstract

Using various techniques, authors have shown that in one-dimensional markets, complex (path-dependent) contracts are generally not optimal for rational consumers. In this paper we generalize these results to a multidimensional Black-Scholes market. In such a market, we discuss optimal contracts for investors who prefer more to less and have a fixed investment horizon T > 0. First, given a desired probability distribution, we give an explicit form of the optimal contract that provides this distribution to the consumer. Second, in the case of risk-averse investors, we are able to propose two ways of improving the design of financial products. In all cases, the optimal payoff can be seen as a path-independent European option that is written on the so-called market portfolio. We illustrate the theory with a few well-known securities and strategies. For example, we show that a buy-and-hold investment strategy can be dominated by a series of power options written on the underlying market portfolio. We also analyze the inefficiency of a widely used portfolio insurance strategy called Constant Proportion Portfolio Insurance.