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 two terms, one is able to capture the implicit transaction costs, and the second the price 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 the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with transaction costs. To better understand how to apply the theory proposed we provide an example with linear and non-linear transaction costs.
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- Hayne E. Leland., 1984.
"Option Pricing and Replication with Transactions Costs,"
Research Program in Finance Working Papers
144, University of California at Berkeley.
- Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
- 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.
- 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.
- 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.
- 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.
- Emmanuel Denis & Yuri Kabanov, 2011.
"Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs,"
- 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.
- 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.
- repec:dau:papers:123456789/4652 is not listed on IDEAS
- George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
- 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.
- 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.
- repec:dau:papers:123456789/9714 is not listed on IDEAS
- repec:dau:papers:123456789/9300 is not listed on IDEAS
- Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
- 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.
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