Superreplication when trading at market indifference prices

Abstract

We study superreplication of European contingent claims in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework, adopting a terminology introduced by Kabanov, Rásonyi and Stricker in the context of models with proportional transaction costs. In our framework, efficient friction amounts to the mild requirement that large positions of the investor potentially lead to large losses, a fact from which we derive the existence of superreplicating strategies. We illustrate that without this condition, there may be no superreplicating strategy with minimal costs. In our main results, we establish efficient friction under a tail condition on the conditional distributions of the traded securities and under an asymptotic condition on the market makers’ risk aversions. Another result asserts that strict monotonicity of the conditional essential infima and suprema of the security prices is also sufficient for efficient friction. We give examples that satisfy the assumptions in our conditions, which include non-degenerate finite sample space models as well as discretely monitored Lévy process models and an affine stochastic volatility model of Barndorff-Nielsen/Shephard type.