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Computing the first passage time density of a time-dependent Ornstein–Uhlenbeck process to a moving boundary |
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| Authors: | C.F. Lo C.H. Hui |
| Affiliation: | aInstitute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong bResearch Department, Hong Kong Monetary Authority, 55/F Two International Finance Centre, 8 Finance Street, Central, Hong Kong |
| Abstract: | In this paper we use the method of images to derive the closed-form formula for the first passage time density of a time-dependent Ornstein–Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation scheme to compute tight upper and lower bounds of the first passage time density through a fixed boundary. |
| Keywords: | Ornstein–Uhlenbeck process Fokker–Planck equation First passage time density Method of images Moving boundary |
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