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

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  • Pospisil, Libor
  • Vecer, Jan
  • Hadjiliadis, Olympia

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.

Suggested Citation

  • Pospisil, Libor & Vecer, Jan & Hadjiliadis, Olympia, 2009. "Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2563-2578, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2563-2578
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    References listed on IDEAS

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