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The Journal of Derivatives

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Analytical Valuation of Exotic Double Barrier Options

Jui-Jane Chang, Hui-Ming Pai and Ting-Pin Wu
The Journal of Derivatives Spring 2021, 28 (3) 97-122; DOI: https://doi.org/10.3905/jod.2020.1.118
Jui-Jane Chang
is an associate professor in the Department of Financial Engineering and Actuarial Mathematics at Soochow University in Taipei, Taiwan
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Hui-Ming Pai
is an associate professor in the Department of Statistics at National Taipei University in New Taipei City, Taiwan
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Ting-Pin Wu
is a professor in the Department of Finance at National Central University in Jhongli City, Taiwan
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Abstract

This article derives the bivariate joint probability distribution functions of a geometric Brownian motion and the extreme values of another geometric Brownian. Based on the probability distribution functions, the authors develop the analytical pricing formulas of three exotic double barrier options (DBOs) with continuously monitored barriers, including rainbow DBOs, protected DBOs, and protected rainbow DBOs. By using the continuity correction of barriers proposed in research by Doobae Jun, the aforementioned pricing formulas can be further extended to price the three exotic DBOs with discretely monitored barriers. Some numerical examples are also provided for end-users to examine the pricing accuracy and efficiency and the properties of the exotic DBOs.

TOPICS: Derivatives, options

Key Findings

  • ▪ This article derives the bivariate joint probability distribution functions of a geometric Brownian motion and the extreme values of another geometric Brownian.

  • ▪ This article develops the analytical pricing formulas of three exotic double barrier options (DBOs) with continuously monitored barriers, including rainbow DBOs, protected DBOs, and protected rainbow DBOs.

  • ▪ By using the continuity correction of barriers proposed in research by Doobae Jun, the three exotic double barrier options with discretely monitored barriers are also developed.

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The Journal of Derivatives: 28 (3)
The Journal of Derivatives
Vol. 28, Issue 3
Spring 2021
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Analytical Valuation of Exotic Double Barrier Options
Jui-Jane Chang, Hui-Ming Pai, Ting-Pin Wu
The Journal of Derivatives Feb 2021, 28 (3) 97-122; DOI: 10.3905/jod.2020.1.118

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Analytical Valuation of Exotic Double Barrier Options
Jui-Jane Chang, Hui-Ming Pai, Ting-Pin Wu
The Journal of Derivatives Feb 2021, 28 (3) 97-122; DOI: 10.3905/jod.2020.1.118
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  • Article
    • Abstract
    • BIVARIATE JOINT DENSITY AND DISTRIBUTION FUNCTIONS
    • THE PRICING OF THREE EXOTIC DBOs
    • THE PRICING OF EXOTIC DBOs WITH DISCRETELY MONITORED BARRIERS
    • NUMERICAL STUDIES
    • CONCLUSIONS
    • ACKNOWLEDGMENTS
    • APPENDIX A
    • APPENDIX B
    • ENDNOTES
    • REFERENCES
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