An Unhedgeable Black–Scholes–Merton Implicit Option?

Alfredo Pereira and M. Sean Tarter
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M. Sean Tarter: Department of Applied Science, William & Mary, Williamsburg, VA 23187, USA

Risks, 2022, vol. 10, issue 7, 1-12

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.

Keywords: Black–Scholes–Merton; hedging; market network; option valuation; portfolio optimization; risk-bearing portfolio managers (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
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