Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices
In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.
|Date of creation:||May 2012|
|Date of revision:||Jun 2013|
|Publication status:||Published in International Journal of Theoretical and Applied Finance, vol. 16, No 1, 2013|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Tomasz R. Bielecki & Igor Cialenco & Zhao Zhang, 2010. "Dynamic Coherent Acceptability Indices and their Applications to Finance," Papers 1010.4339, arXiv.org, revised May 2011.
- Alexander S. Cherny & Dilip B. Madan, 2006. "Pricing and hedging in incomplete markets with coherent risk," Papers math/0605064, arXiv.org.
- Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
- PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
- Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612.
- 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.
- Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
- William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
- repec:crs:wpaper:9513 is not listed on IDEAS
- Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
- 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.
- 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.
- repec:dau:papers:123456789/5630 is not listed on IDEAS
- Alexander Cherny, 2007. "Pricing and hedging European options with discrete-time coherent risk," Finance and Stochastics, Springer, vol. 11(4), pages 537-569, October.
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