Continuity Theorems in Boundary Crossing Problems for Diffusion Processes

Konstantin A. Borovkov (), Andrew N. Downes () and Alexander A. Novikov ()
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Konstantin A. Borovkov: Univ. of Melbourne, Dept. of Mathematics and Statistics
Andrew N. Downes: Univ. of Melbourne, Dept. of Mathematics and Statistics
Alexander A. Novikov: The University of Technology, Dept. of Mathematical Sciences

A chapter in Contemporary Quantitative Finance, 2010, pp 335-351 from Springer

Abstract: Abstract Computing the probability for a given diffusion process to stay under a particular boundary is crucial in many important applications including pricing financial barrier options and defaultable bonds. It is a rather tedious task that, in the general case, requires the use of some approximation methodology. One possible approach to this problem is to approximate given (general curvilinear) boundaries with some other boundaries of a form enabling one to relatively easily compute the boundary crossing probability. We discuss results on the accuracy of such approximations for both the Brownian motion process and general time-homogeneous diffusions and also some contiguous topics.

Keywords: Brownian Motion; Underlying Asset; Price Formula; Barrier Option; Bessel Process (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03479-4_17

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DOI: 10.1007/978-3-642-03479-4_17

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