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On a pricing problem for a multi-asset option with general transaction costs

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  • Pablo Amster
  • Andres P. Mogni

Abstract

We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is multi-dimensional since it involves different underlying assets; on the other hand, the transaction costs are not assumed to be constant (i.e. a fixed proportion of the traded quantity). In this work, we generalize Leland's condition and prove the existence of a viscosity solution for the corresponding fully nonlinear initial value problem using Perron method. Moreover, we develop a numerical ADI scheme to find an approximated solution. We apply this method on a specific multi-asset derivative and we obtain the option price under different pricing scenarios.

Suggested Citation

  • Pablo Amster & Andres P. Mogni, 2017. "On a pricing problem for a multi-asset option with general transaction costs," Papers 1704.02036, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1704.02036
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. 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 637-654, May-June.
    3. Indranil SenGupta, 2014. "Option Pricing with Transaction Costs and Stochastic Interest Rate," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(5), pages 399-416, November.
    4. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
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