Journal article
Cost-efficient contingent claims with market frictions
Mathematics and financial economics, Vol.10(1), pp.87-111
01/01/2016
DOI: 10.1007/s11579-015-0151-7
Abstract
In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps in J Econ Theory 20(3): 381408, 1979). Dybvig (J Bus 61(3):369-393, 1988; Rev Financ Stud 1(1):67-88, 1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we look at extending Dybvig's ideas to complete markets with imperfections represented by a nonlinear pricing rule (e.g., due to bid-ask spreads). We consider an investor in a securities market where the pricing rule is "law-invariant" with respect to a capacity (e.g., Choquet pricing as in Araujo et al. in Econ Theory 49(1):1-35, 2011; Chateauneuf et al. in Math Financ 6(3):323-330, 1996; Chateauneuf and Cornet in Submodular financial markets with frictions, 2015; Cerreia-Vioglio et al. in J Econ Theory 157:730-762, 2015). The investor holds a security with a random payoff X and his problem is that of buying the cheapest contingent claim Y on X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called cost-efficient. If the capacity satisfies standard continuity and a property called strong diffuseness introduced in Ghossoub (Math Op Res 40(2):429-445, 2015), we show the existence and monotonicity of cost-efficient claims, in the sense that a cost-efficient claim is anti-comonotonic with the underlying security's payoff X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit analytical form for a cost-efficient claim.
Details
- Title: Subtitle
- Cost-efficient contingent claims with market frictions
- Creators
- Mario Ghossoub - Imperial College London
- Resource Type
- Journal article
- Publication Details
- Mathematics and financial economics, Vol.10(1), pp.87-111
- DOI
- 10.1007/s11579-015-0151-7
- ISSN
- 1862-9679
- eISSN
- 1862-9660
- Publisher
- Springer Nature
- Number of pages
- 25
- Language
- English
- Date published
- 01/01/2016
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985179849802771
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