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On the Applicability of the Black-Scholes Model to the Inverse Quantity of Price (Under Peer-Review)

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  • Tahara, Hiroki

    (Jan Academy)

Abstract

The aim of this article is to prove the applicability of the Black-Scholes model to the inverse quantity of price, which is the generalization of the applicability of the model to foreign currency. This issue can be formulated as the discussion whether there exists the set of real numbers as the drift and the volatility about the inverse quantity satisfying a certain system of stochastic differential equations. Solving the equations in terms of such real numbers reveals not only the existence but also that the expression is uniquely determined and has a very beautiful symmetry.

Suggested Citation

  • Tahara, Hiroki, 2020. "On the Applicability of the Black-Scholes Model to the Inverse Quantity of Price (Under Peer-Review)," OSF Preprints fgnca_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:fgnca_v1
    DOI: 10.31219/osf.io/fgnca_v1
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    References listed on IDEAS

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    1. Andreas Schrimpf & Vladyslav Sushko, 2019. "Sizing up global foreign exchange markets," BIS Quarterly Review, Bank for International Settlements, December.
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    3. Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
    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. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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