2013/10/11 by Peter Bank, Bank, Peter, Selim Gökay +1
Economics, Econometrics and Finance · #52A41 #60G35 #90C30 #91G20 #97M30 #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #msc:52A41 #msc:60G35 #msc:90C30 #msc:91G20 #msc:97M30 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1310.3113
arxiv created 2013/10/11 · openalex publication_date 2013/10/11 · arxiv updated 2013/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study superreplication of European contingent claims in discrete time 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, Rasonyi, and Stricker in the context of models with proportional transaction costs. In our framework, efficient friction ensures that large positions of the investor may 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 result, we establish efficient friction under a tail condition on the conditional distributions of the traded securities and under an asymptotic criterion on risk aversions of the market makers. Another result asserts that strict monotonicity of the conditional essential infima and suprema of the security prices is 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 Levy processes and an affine stochastic volatility model of Barndorff-Nielsen-Shepard type.