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Consistent price systems and face-lifting pricing under transaction costs

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Author Info
Paolo Guasoni
Mikl\'os R\'asonyi
Walter Schachermayer
Abstract

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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File URL: http://arxiv.org/abs/0803.4416
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0803.4416.

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Date of creation: Mar 2008
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Publication status: Published in Annals of Applied Probability 2008, Vol. 18, No. 2, 491-520
Handle: RePEc:arx:papers:0803.4416

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54. [Downloadable!] (restricted)
  2. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October. [Downloadable!] (restricted)
  3. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Blackwell Publishing, vol. 7(1), pages 95-105. [Downloadable!] (restricted)
  4. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273. [Downloadable!] (restricted)
  5. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June. [Downloadable!] (restricted)
  6. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September. [Downloadable!] (restricted)
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  7. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December. [Downloadable!] (restricted)
  8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248. [Downloadable!] (restricted)
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  1. Erhan Bayraktar & Hasanjan Sayit, 2008. "On the Stickiness Property," Quantitative Finance Papers 0801.0718, arXiv.org, revised Sep 2009. [Downloadable!]
  2. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October. [Downloadable!] (restricted)
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