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Finance

2014/2 (Vol. 35)


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Abstract

English

In this paper, we give an explicit representation of the lowest cost strategy to achieve a given payoff distribution (that we call “cost-efficient” strategy). For any inefficient strategy, we are able to construct financial derivatives which dominate in the sense of first-order or second-order stochastic dominance. We highlight the connections between cost-efficiency and dependence. This allows us to extend the theory to deal with state-dependent constraints to better reflect real-world preferences. We show in particular that path-dependent strategies (although inefficient in the Black Scholes setting) may become optimal in the presence of state-dependent constraints.

Outline

  1. Introduction
  2. Assumptions and Definitions
  3. Cost-Efficient Payoffs
    1. Characterization
    2. Black Scholes Market
  4. Agents with state-independent preferences
  5. Examples
    1. Forward Contract
    2. Put options
    3. Path-dependent examples
      1. Lookback options
      2. Geometric Asian options
  6. Cost-efficiency with state-dependent constraints
    1. Constrained cost-efficient payoffs
    2. 6.2. A finite number of constraints
    3. Tail constraints
  7. Summary and Conclusion

To cite this article

Carole Bernard, Phelim P. Boyle, Steven Vanduffel, “ Explicit Representation of Cost-Efficient Strategies ”, Finance 2/2014 (Vol. 35) , p. 5-55
URL : www.cairn.info/revue-finance-2014-2-page-5.htm.

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