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

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  • Carole Bernard
  • Mateusz Maj
  • Steven Vanduffel

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.

Suggested Citation

  • Carole Bernard & Mateusz Maj & Steven Vanduffel, 2011. "Improving the Design of Financial Products in a Multidimensional Black-Scholes Market," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 77-96.
    • Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:77-96
    DOI: 10.1080/10920277.2011.10597610
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    Cited by:

    1. Carole Bernard & Jit Seng Chen & Steven Vanduffel, 2014. "Optimal portfolios under worst-case scenarios," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 657-671, April.
    2. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    3. Jonathan Ansari & Ludger Rüschendorf, 2018. "Ordering Results for Risk Bounds and Cost-efficient Payoffs in Partially Specified Risk Factor Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 817-838, September.

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