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Optimal exercise of American puts with transaction costs under utility maximization

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  • Lu, Xiaoping
  • Yan, Dong
  • Zhu, Song-Ping

Abstract

American option pricing plays an essential role in quantitative finance and has been extensively studied in the past. However, how transaction costs affect the American option price, particularly the most important feature of American options, the optimal exercise price, is much less investigated. It is primarily because such a study must be conducted under an incomplete market, which presents additional difficulties on top of an already difficult nonlinear mathematical problem. This paper attempts to provide a supplement study in this area by analyzing the optimal exercise price of an American option in addition to the option price itself in the presence of transaction costs through a utility-based approach. With a computationally efficient numerical scheme, we are able to demonstrate clearly how the optimal exercise price should be calculated and consequently how the option prices for the buyer and writer as well as the early exercise decision are affected by the inclusion of transaction cost.

Suggested Citation

  • Lu, Xiaoping & Yan, Dong & Zhu, Song-Ping, 2022. "Optimal exercise of American puts with transaction costs under utility maximization," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    • Handle: RePEc:eee:apmaco:v:415:y:2022:i:c:s0096300321007682
    DOI: 10.1016/j.amc.2021.126684
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    2. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    3. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    4. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    5. Damgaard, Anders, 2003. "Utility based option evaluation with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 667-700, February.
    6. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    7. Benjamin Mohamed, 1994. "Simulations of transaction costs and optimal rehedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 49-62.
    8. Guo, Ivan & Zhu, Song-Ping, 2017. "Equal risk pricing under convex trading constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 136-151.
    9. Damgaard, Anders, 2006. "Computation of reservation prices of options with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 415-444, March.
    10. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    11. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    12. Maxim Bichuch, 2014. "Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment," Finance and Stochastics, Springer, vol. 18(3), pages 651-694, July.
    13. Xin-Jiang He & Song-Ping Zhu, 2020. "A revised option pricing formula with the underlying being banned from short selling," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 935-948, June.
    14. Song-Ping Zhu, 2006. "A New Analytical Approximation Formula For The Optimal Exercise Boundary Of American Put Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1141-1177.
    15. 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.
    16. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    17. 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.
    18. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
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