First Exit Time from a Corridor

摘要

In this paper, closed form results are provided for the distribution of the first exit time of Brownian motion with drift from various sequences of two-sided boundaries called "corridors", in reference to a certain class of options traded in the financial markets. The numerical evaluation of the given formulae can be done with the accuracy and the efficiency required for all practical purposes. The sensitivity of the survival probability of Brownian motion under and above these time-varying upper and lower steps is analysed with regard to key parameters. As closed form results become more and more cumbersome with increasing dimension, a semi-analytical scheme is introduced to deal with higher dimension, based on explicit analytical representations of the density function of a multivariate normal random vector.