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Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment

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  • Maxim Bichuch
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    Abstract

    We price a contingent claim liability using the utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of positive proportional transaction cost in two cases with and without a contingent claim liability. Using the computations from the heuristic argument in Whalley & Wilmott we provide a rigorous derivation of the asymptotic expansion of the value function in powers of the transaction cost parameter around the known value function for the case of zero transaction cost in both cases with and without a contingent claim liability. Additionally, using utility indifference method we derive an asymptotic expansion of the price of the contingent claim liability. In both cases, we also obtain a "nearly optimal" strategy, whose expected utility asymptotically matches the leading terms of the value function.

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    File URL: http://arxiv.org/pdf/1112.3012
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    Paper provided by arXiv.org in its series Papers with number 1112.3012.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.3012

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    1. Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(8-9), pages 1353-1376, June.
    2. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(2), pages 245-263, October.
    4. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, American Finance Association, vol. 46(2), pages 577-95, June.
    5. George M. Constantinides & Thaleia Zariphopoulou, . "Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs and General Preferences," CRSP working papers, Center for Research in Security Prices, Graduate School of Business, University of Chicago 347, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    6. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, Springer, vol. 2(4), pages 369-397.
    7. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, American Finance Association, vol. 47(1), pages 271-93, March.
    8. Freddy Delbaen & Yuri M. Kabanov & Esko Valkeila, 2002. "Hedging under Transaction Costs in Currency Markets: a Discrete-Time Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(1), pages 45-61.
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