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An Unhedgeable Black–Scholes–Merton Implicit Option?

Author

Listed:
  • Alfredo M. Pereira

    (Department of Economics, William & Mary, Williamsburg, VA 23187, USA)

  • M. Sean Tarter

    (Department of Applied Science, William & Mary, Williamsburg, VA 23187, USA)

Abstract

In this paper, we focus on an implicit assumption in the BSM framework that limits the scope of market network connections to seeking gains in the currency basis, i.e., on trading strategies between the numeraire and the stock and between the numeraire and the option, separately. We relax this assumption and derive the equivalent of the standard BSM approach under a more general market network framework in order to assess its implications. In doing so, we find that it is not possible to hedge on an implicit option that allows one to directly trade the option and stock. This represents a potential challenge to the BSM framework, since the missing market network connection provides a potentially useful mechanism for risk-bearing portfolio managers to alter their portfolios.

Suggested Citation

  • Alfredo M. Pereira & M. Sean Tarter, 2022. "An Unhedgeable Black–Scholes–Merton Implicit Option?," Risks, MDPI, vol. 10(7), pages 1-12, June.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:7:p:134-:d:851550
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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. Bernard Dumas & Andrew Lyasoff, 2012. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," Journal of Finance, American Finance Association, vol. 67(5), pages 1897-1941, October.
    3. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    4. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    5. J. S. Kennedy & P. A. Forsyth & K. R. Vetzal, 2009. "Dynamic Hedging Under Jump Diffusion with Transaction Costs," Operations Research, INFORMS, vol. 57(3), pages 541-559, June.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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