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Risk minimization for game options in markets imposing minimal transaction costs

Published online by Cambridge University Press:  19 September 2016

Yan Dolinsky*
Affiliation:
The Hebrew University of Jerusalem
Yuri Kifer*
Affiliation:
The Hebrew University of Jerusalem
*
* Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. Email address: [email protected]
** Postal address: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 9190401, Israel. Email address: [email protected]

Abstract

We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction cost. We prove that in the continuous-time Black‒Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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