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Efficient Option Pricing with Transaction Costs

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Author Info
Michael Monoyios ()
Alberto Montagnoli
Abstract

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor's basic portfolio selection problem, without the insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete time Markov chain approximation to a continuous time singular stochastic optimal control problem. A general de nition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed.

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File URL: http://www.brunel.ac.uk/329/efwps/02-22.pdf
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Publisher Info
Paper provided by Economics and Finance Section, School of Social Sciences, Brunel University in its series Economics and Finance Discussion Papers with number 02-22.

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Length: 23 pages
Date of creation: Jul 2002
Date of revision:
Handle: RePEc:bru:bruedp:02-22

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Postal: Brunel University, Uxbridge, Middlesex UB8 3PH, UK

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  1. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54. [Downloadable!] (restricted)
  2. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May. [Downloadable!] (restricted)
  3. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482. [Downloadable!] (restricted)
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  5. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March. [Downloadable!] (restricted)
  6. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December. [Downloadable!] (restricted)
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  7. D. Lamberton & H. Pham & M. Schweizer, . "Local Risk-Minimization under Transaction Costs," Sonderforschungsbereich 373 1998-18, Humboldt Universitaet Berlin.
  8. Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1353-1376, June. [Downloadable!] (restricted)
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