Explicit formulae for the valuation of European options with price impacts

Julio César Rodríguez-Burgos (), Gerardo Hernández-del-Valle and Héctor Jasso-Fuentes ()
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Julio César Rodríguez-Burgos: CEMLA
Héctor Jasso-Fuentes: CINVESTAV–IPN
Authors registered in the RePEc Author Service: Julio César Rodríguez Burgos

No 04/2023, CEMLA Working Paper Series from CEMLA

Abstract: In this work, we analyze the effect of trading a large position of vanilla European options where the underlying price S follows a multi-period binomial model. Due to the large size of the transaction, we expect that not only the price of the derivative but also the price of the underlying S, should be subject to price impacts. As a byproduct, the valuation of derivatives should be analyzed taking into account the latter effects. In order to do so, besides assuming that the price process S can be modeled using a multi-period binomial model, we also assume that the trading impacts affect the price S in a multiplicative way. Furthermore, our analysis is carried out in discrete time to better trace the effects of price impacts, and conclude for instance, that the strike price should be itself a function of the size of the trade, and the parameterized market impacts. We provide explicit formulae for the price of European options under market impacts as well as numerical examples to illustrate our results. Code in the statistical package R can be provided upon request.

Keywords: Price impacts; valuation of derivatives; multi-period binomial model. (search for similar items in EconPapers)
JEL-codes: C02 C61 C65 G12 (search for similar items in EconPapers)
Pages: 21
Date: 2023-04
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