Corridor options and arc-sine law

Abstract

We study a generalization of the arc-sine law. In particular we provide new results about the distribution of the time spent by a BM with drift inside a band, giving the Laplace transform of the characteristic function. If one of the extremes of the band goes to infinity, our formula agrees with the results given in Akahori and Takàcs.We apply these results to the pricing of exotic option contracts known as corridor derivatives.We then discuss the inversion problem comparing different numerical methods.