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A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance

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  • Ballestra, Luca Vincenzo
  • Pacelli, Graziella
  • Radi, Davide

Abstract

We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations.

Suggested Citation

  • Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 330-344.
    • Handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:330-344
    DOI: 10.1016/j.physa.2016.07.016
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    Cited by:

    1. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.

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