Implicit transaction costs and the fundamental theorems of asset pricing
This paper studies arbitrage pricing theory in ?financial markets with transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Transaction costs are composed of three terms, one is able to capture the implicit transaction costs, the second the price impact and the last the bid-ask spread impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having c?adl?ag (right-continuous with left limits) and c?agl?ad (left-continuous with right limits) paths of bounded quadratic variation and of ?finitely many jumps. That is, c?adl?ag and c?agl?ad predictable trading strategies of infinite variation, with?finitely many jumps and of ?finite quadratic variation are allowed in our setting. Restricting ourselves to c?agl?ad predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that, in presence of only mid and bid-ask spread price impact, when this probability measure is unique, any contingent claim in the market is hedgeable in an L2-sense. To better understand how to apply the theory proposed we provide an example with linear transaction costs.
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- Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
- Yuri M. Kabanov & (*), Mher M. Safarian, 1997.
"On Leland's strategy of option pricing with transactions costs,"
Finance and Stochastics,
Springer, vol. 1(3), pages 239-250.
- Y. M. Kabanov & M. Safarian, 1995. "On Leland's Strategy of Option Pricing with Transaction Costs," SFB 373 Discussion Papers 1995,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
- Summers, L.H. & Summers, V.P., 1989. "When Financial Markets Work Too Well : A Cautious Case For A Securities Transactions Tax," Papers t12, Columbia - Center for Futures Markets.
- Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
- Leland, Hayne E, 1985.
" Option Pricing and Replication with Transactions Costs,"
Journal of Finance,
American Finance Association, vol. 40(5), pages 1283-1301, December.
- Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
- George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
- Guasoni, Paolo & Lépinette-Denis, Emmanuel & Rásonyi, Miklós, 2012.
"The fundamental theorem of asset pricing under transaction costs,"
Economics Papers from University Paris Dauphine
123456789/9300, Paris Dauphine University.
- Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
- Emmanuel Denis & Yuri Kabanov, 2012.
"Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs,"
Finance and Stochastics,
Springer, vol. 16(1), pages 135-154, January.
- Lépinette-Denis, Emmanuel & Kabanov, Yuri, 2012. "Consistent Price Systems and Arbitrage Opportunities of the Second Kind in Models with Transaction Costs," Economics Papers from University Paris Dauphine 123456789/4652, Paris Dauphine University.
- repec:dau:papers:123456789/9714 is not listed on IDEAS
- Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
- Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
- Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
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