Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups

Libor Pospisil, Jan Vecer and Olympia Hadjiliadis

Stochastic Processes and their Applications, 2009, vol. 119, issue 8, 2563-2578

Abstract: 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.

Keywords: Diffusion; process; Drawdowns; and; drawups; Stopping; time (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (28)

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