Corridor options and arc-sine law

Gianluca Fusai

25 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

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.

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References

2007Brownian Motion and Stochastic Calculus 2016“Options, Futures, and Other Derivatives”1979Martingales and arbitrage in multiperiod securities markets 1991Brownian motion and stochastic calculus 1996Handbook of Brownian Motion — Facts and Formulae 1977Options: A Monte Carlo approach 1994Multidimensional Transform Inversion with Applications to the Transient M/G/1 Queue 1995The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options

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