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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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    1. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    2. Claudia Ribeiro & Nick Webber, 2006. "Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 333-352.
    3. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    4. Hamza Hanbali & Daniel Linders, 2019. "American-type basket option pricing: a simple two-dimensional partial differential equation," Quantitative Finance, Taylor & Francis Journals, vol. 19(10), pages 1689-1704, October.
    5. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    6. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    7. Lee, Hangsuck & Lee, Minha & Ko, Bangwon, 2022. "A semi-analytic valuation of two-asset barrier options and autocallable products using Brownian bridge," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    8. Chaeyoung Lee & Jisang Lyu & Eunchae Park & Wonjin Lee & Sangkwon Kim & Darae Jeong & Junseok Kim, 2020. "Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method," Mathematics, MDPI, vol. 8(3), pages 1-13, February.
    9. Barbara Goetz & Marcos Escobar & Rudi Zagst, 2017. "Two asset-barrier option under stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(6), pages 520-546, November.
    10. Emmanuel Gobet, 2009. "Advanced Monte Carlo methods for barrier and related exotic options," Post-Print hal-00319947, HAL.
    11. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    12. Lee, Hangsuck & Ahn, Soohan & Ko, Bangwon, 2019. "Generalizing the reflection principle of Brownian motion, and closed-form pricing of barrier options and autocallable investments," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    13. Andrew Ming-Long Wang & Yu-Hong Liu & Yi-Long Hsiao, 2009. "Barrier option pricing: a hybrid method approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 341-352.
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    Keywords

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    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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