First hitting time of integral diffusions and applications |
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Authors: | Zhenyu Cui Duy Nguyen |
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Institution: | 1. School of Business, Stevens Institute of Technology, Hoboken, New Jersy, USA;2. Department of Mathematics, Marist College, Poughkeepsie, New York, USA |
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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. |
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Keywords: | Asian options first hitting time Laplace transform stochastic time change volatility derivative |
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