Closed form valuation of barrier options with stochastic barriers

Tristan Guillaume ()
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Tristan Guillaume: Université de Cergy-Pontoise

Annals of Operations Research, 2022, vol. 313, issue 2, No 19, 1050 pages

Abstract: Abstract This article deals with the computation of the probability, for a GBM (geometric Brownian motion) process, to hit sequences of one-sided stochastic boundaries defined as GBM processes, over a closed time interval. Explicit formulae are obtained, allowing the analytical valuation of all the main kinds of barrier options in a much more general setting than the usual one assuming constant or time-dependent, deterministic barriers. The numerical implementation of all stated formulae is shown to be easy, fast and accurate. The practical applications are potentially substantial, since barrier options play a major role in quantitative finance, not only as intensively traded contracts on their own, but also as the building blocks of a large variety of structured products. Barrier options are also an important tool in financial modelling, used to measure default risk in the so-called “structural” models.

Keywords: Boundary crossing probability; First passage time probability; Barrier option; Stochastic barrier; Option valuation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-020-03860-w

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