Explicit formulae for the valuation of European options with price impacts

In this work, we examine the consequences of trading a large position in vanilla European options within a multi-period binomial model framework for the underlying asset price, S. Given the significant size of the transaction, we expect both the derivative's price and the underlying asset'...

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Bibliographic Details
Published inThe Journal of finance and data science Vol. 10; p. 100133
Main Authors Hernández-del-Valle, Gerardo, Rodríguez-Burgos, Julio César, Jasso-Fuentes, Héctor
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2024
Subjects
Multi-period binomial model
Price impacts
Valuation of derivatives
Valuation of derivatives
C65
C02
91B24
91G30
G12
91B70
91G15
Multi-period binomial model
Price impacts
C61
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Summary:In this work, we examine the consequences of trading a large position in vanilla European options within a multi-period binomial model framework for the underlying asset price, S. Given the significant size of the transaction, we expect both the derivative's price and the underlying asset's price to be affected by market impacts. Consequently, derivative valuation should incorporate these effects. To address this, we not only utilize a multi-period binomial model to represent the price process S but also incorporate trading impacts in a multiplicative manner. Moreover, we conduct our analysis in discrete time to better capture the influence of price impacts. Our findings suggest, for instance, that the strike price should be determined by both the trade's magnitude and parameterized market impacts. We present explicit formulas for European option prices under market impacts and offer numerical examples to elucidate our findings. Upon request, we can provide code implemented in the statistical package R.
ISSN:2405-9188
2405-9188
DOI:10.1016/j.jfds.2024.100133