Some Sequential Boundary Crossing Results for Geometric Brownian Motion and Their Applications in Financial Engineering | Zendy

Tristan Guillaume | Zendy

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Some Sequential Boundary Crossing Results for Geometric Brownian Motion and Their Applications in Financial Engineering

Author(s) -

Tristan Guillaume

Publication year - 2011

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.5402/2011/120253

Subject(s) - geometric brownian motion , piecewise , brownian motion , valuation (finance) , boundary (topology) , constant (computer programming) , mathematics , mathematical finance , mathematical analysis , mathematical economics , mathematical optimization , computer science , finance , economics , diffusion process , statistics , knowledge management , innovation diffusion , programming language

This paper provides new explicit results for some boundary crossing distributions in a multidimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and look-back options.

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