Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk
According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version. The axiomatic of TCPP allows for the construction of pricing procedures extending the dynamics of reference assets and calibrated on option prices for a reference family of options. We characterize such TCPP in terms of their dual representation. Such TCPP provide new bounds compatible with the observed bid and ask prices for the reference options and reducing the bid ask spreads for the other financial instruments.
References listed on IDEAS
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.:
- Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
- Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Economics Papers from University Paris Dauphine 123456789/13388, Paris Dauphine University.
- Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
- Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627.
- Jouini, Elyes, 2000.
"Price functionals with bid-ask spreads: an axiomatic approach,"
Journal of Mathematical Economics,
Elsevier, vol. 34(4), pages 547-558, December.
- Elyès Jouini, 1999. "Price Functionals with Bid-Ask Spreads: An Axiomatic Approach," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-038, New York University, Leonard N. Stern School of Business-.
- Elyès Jouini, 1997. "Price Functionals with Bid-Ask Spreads : An Axiomatic Approach," Working Papers 97-05, Centre de Recherche en Economie et Statistique.
- Klöppel Susanne & Schweizer Martin, 2007. "Dynamic utility-based good deal bounds," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 25, October.
- Shige Peng, 2006. "Modelling Derivatives Pricing Mechanisms with Their Generating Functions," Papers math/0605599, arXiv.org.
- Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 36, July.
- U. �etin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Jocelyne Bion-Nadal, 2008. "Time Consistent Dynamic Limit Order Books Calibrated on Options," Papers 0809.3824, arXiv.org.
- Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
- Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
- Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
- Bion-Nadal, Jocelyne, 2009. "Time consistent dynamic risk processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 633-654, February.
- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
- Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
- Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161.
- Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
- Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- repec:fth:inseep:9513 is not listed on IDEAS
- Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
- Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.
- Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
- Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
- L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
- Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:45:y:2009:i:11:p:738-750. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.