First hitting time of integral diffusions and applications

Zhenyu Cui, Duy Nguyen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study the first hitting time of integral functionals of time-homogeneous diffusions, and characterize their Laplace transforms through a stochastic time change. We obtain explicit expressions of the Laplace transforms for the geometric Brownian motion (GBM) and the mean-reverting GBM process. We also introduce a novel probability identity based on an independent exponential randomization and obtain explicit Laplace transforms of the price of arithmetic Asian options and other derivative prices that non-linearly depend on the integral diffusions. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.

Original languageEnglish
Pages (from-to)376-391
Number of pages16
JournalStochastic Models
Volume33
Issue number3
DOIs
StatePublished - 3 Jul 2017

Keywords

  • Asian options
  • Laplace transform
  • first hitting time
  • stochastic time change
  • volatility derivative

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