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European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs

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  • Valeri Zakamouline

    (Norwegian School of Economics & Business Administration)

Abstract

In this paper we extend the utility based option pricing and hedging approach, pioneered by Hodges and Neuberger (1989) and further developed by Davis, Panas and Zariphopoulou (1993), for the market where each transaction has a fixed cost component. We present a model, where investors have a CARA utility, and derive some properties of reservation option prices. We suggest and implement discretization schemes for computing the reservation option prices. The numerical results of option pricing and hedging are presented for the case of European call options and the investors with different levels of ARA. We also try to reconcile our findings with such empirical pricing bias as the volatility smile.

Suggested Citation

  • Valeri Zakamouline, 2003. "European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs," Finance 0311009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0311009
    Note: Type of Document - pdf; prepared on WinXP; pages: 43; figures: 6
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    References listed on IDEAS

    as
    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. Benjamin Mohamed, 1994. "Simulations of transaction costs and optimal rehedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 49-62.
    3. (*), Thaleia Zariphopoulou & George M. Constantinides, 1999. "Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences," Finance and Stochastics, Springer, vol. 3(3), pages 345-369.
    4. 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.
    5. 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.
    6. Dermody, Jaime Cuevas & Prisman, Eliezer Z., 1993. "No Arbitrage and Valuation in Markets with Realistic Transaction Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 65-80, March.
    7. Jerome F. Eastham & Kevin J. Hastings, 1988. "Optimal Impulse Control of Portfolios," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 588-605, November.
    8. 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.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    option pricing; transaction costs; stochastic control; 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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