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An Unhedgeable Black-Scholes-Merton Implicit Option?
Version 1
: Received: 9 May 2022 / Approved: 17 May 2022 / Online: 17 May 2022 (03:05:52 CEST)
A peer-reviewed article of this Preprint also exists.
Pereira, A.M.; Tarter, M.S. An Unhedgeable Black–Scholes–Merton Implicit Option? Risks 2022, 10, 134. Pereira, A.M.; Tarter, M.S. An Unhedgeable Black–Scholes–Merton Implicit Option? Risks 2022, 10, 134.
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 the 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.
Keywords
Black-Scholes-Merton; hedging; market network; option valuation; portfolio optimization; risk-bearing portfolio managers
Subject
Business, Economics and Management, Finance
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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