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Explicit formulae for the valuation of European options with price impacts

Author

Listed:
  • Julio César Rodríguez-Burgos

    (CEMLA)

  • Gerardo Hernández-del-Valle

    (CEMLA)

  • Héctor Jasso-Fuentes

    (CINVESTAV–IPN)

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.

Suggested Citation

  • Julio César Rodríguez-Burgos & Gerardo Hernández-del-Valle & Héctor Jasso-Fuentes, 2023. "Explicit formulae for the valuation of European options with price impacts," CEMLA Working Paper Series 04/2023, CEMLA.
    • Handle: RePEc:cml:wpseri:04
    as

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    References listed on IDEAS

    as
    1. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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    More about this item

    Keywords

    Price impacts; valuation of derivatives; multi-period binomial model.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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