First hitting time of integral diffusions and applications. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Cui, Zhenyu; Nguyen, Duy
• Is Part Of: Stochastic models. Volume 33:Issue 3(2017)
• Page Start: 376
• Page End: 391
• Publication Date: 2017-07-03
• Subjects: Asian options -- first hitting time -- Laplace transform -- stochastic time change -- volatility derivative; 60G44 -- 91B70 -- 91B25; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2017.1300920
• Languages: English
• ISSNs: 1532-6349

Abstract

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.