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Valuing three-asset barrier options and autocallable products via exit probabilities of Brownian bridge

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  • Lee, Hangsuck
  • Ha, Hongjun
  • Kong, Byungdoo
  • Lee, Minha

Abstract

This paper discusses pricing barrier options and autocallable structured products on underlying three assets via exit probabilities of a three-dimensional Brownian bridge. We derive the marginal exit and bivariate co-exit probabilities. Despite the impossibility of finding an analytical trivariate co-exit probability, its calculation is not regarded as a purely numerical problem. After specifying the component to be numerically evaluated, logistic regression with the Monte Carlo method is adopted to predict it. Extensive numerical experiments of calculating the exit probability of the three-dimensional Brownian motion and pricing complex products demonstrate the effectiveness and efficiency of our approach.

Suggested Citation

  • Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo & Lee, Minha, 2024. "Valuing three-asset barrier options and autocallable products via exit probabilities of Brownian bridge," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    • Handle: RePEc:eee:ecofin:v:73:y:2024:i:c:s1062940824000998
    DOI: 10.1016/j.najef.2024.102174
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    References listed on IDEAS

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    More about this item

    Keywords

    Exit probability; Three-dimensional Brownian bridge; Barrier options; Autocallable structured product;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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