Consistent price systems and face-lifting pricing under transaction costs

Details Consistent price systems and face-lifting pricing under transaction costs Consistent price systems and face-lifting pricing under transaction costs

2008-03-31

arxiv.org/abs/0803.4416v1

Annals of Applied Probability 2008, Vol. 18, No. 2, 491-520

Economy

Quantitative Finance

Pricing of Securities

Published in at http://dx.doi.org/10.1214/07-AAP461 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP461

In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion. Using the constructed price systems, we show, under very general assumptions, the following ``face-lifting'' result: the asymptotic superreplication price of a European contingent claim $g(S_T)$ equals $\hat{g}(S_0)$, where $\hat{g}$ is the concave envelope of $g$ and $S_t$ is the price of the asset at time $t$. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.

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