On the put-call duality of the game options
DOI: https://doi.org/10.3846/mma.2026.24619Abstract
The purpose of this paper is to obtain a duality between the game put and call options assuming three component penalties – proportion of the usual option payoff, shares of the underlying asset, and a fixed amount. We examine separately the cases of finite and infinite maturities. For the perpetual options, we need to derive a polynomial-style equations for the optimal boundaries. We prove the existence and uniqueness of their solutions as well as provide a method for their deriving. This result is important in itself since the current literature in the field is based on inverting of several functions or on solving of non-linear systems which may lead to some computational difficulties and significant errors for extreme parameter values. Furthermore, the duality is established under a finite time horizon too. It is important to note that this duality does not hold under the classical assumption of a fixed penalty.
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put-call duality, game options, optimal boundaries, polynomial-style formula, pricingHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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