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American Option Pricing with Transaction Costs

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  • Valeri Zakamouline

    (Norwegian School of Economics & Business Administration)

Abstract

In this paper we examine the problem of finding investors' reservation option prices and corresponding early exercise policies of American- style options in the market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model, where investors have a CARA utility, and derive some properties of reservation option prices. We discuss the numerical algorithm and propose a new formulation of the problem in terms of quasi-variational HJB inequalities. Based on our formulation, we suggest original discretization schemes for computing reservation prices of American-style option. The discretization schemes are then implemented for computing prices of American put and call options. We examine the effects on the reservation option prices and the corresponding early exercise policies of varying the investor's ARA and the level of transaction costs. We find that in the market with transaction costs the holder of an American-style option exercises this option earlier as compared to the case with no transaction costs. This phenomenon concerns both put and call options written on a non-dividend paying stock. The higher level the transaction costs is, or the higher risk avers the option holder is, the earlier an American option is exercised.

Suggested Citation

  • Valeri Zakamouline, 2003. "American Option Pricing with Transaction Costs," Finance 0311012, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0311012
    Note: Type of Document - pdf; prepared on WinXP; pages: 51; figures: 11
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0311/0311012.pdf
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    3. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    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 637-654, May-June.
    5. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324, July.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Valeri Zakamouline, 2004. "A Unified Approach to Portfolio Optimization with Linear Transaction Costs," GE, Growth, Math methods 0404003, University Library of Munich, Germany, revised 28 Apr 2004.

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    More about this item

    Keywords

    option pricing; transaction costs; stochastic control; optimal stopping; Markov chain approximation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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