Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups
نویسندگان
چکیده
This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that a drawdown of size a precedes a drawup of size b and vice versa. The results are applied to several examples of diffusion processes, such as drifted Brownian motion, Ornstein–Uhlenbeck process, and Cox–Ingersoll–Ross process. c © 2009 Elsevier B.V. All rights reserved. MSC: primary 91B28; secondary 60G44
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