TITLE:
Constrained Wiener Processes and Their Financial Applications
AUTHORS:
Andrew Leung
KEYWORDS:
Wiener Process, Exotic Options, Method of Images, Heat Equation
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.8 No.4,
November
26,
2018
ABSTRACT: The extrema of Wiener processes are relevant to the pricing of so-called exotic
options, which have many financial applications. The probability densities
of such extrema are well known for one dimensional Wiener processes. We
employ elementary methods to derive analytical expressions for the densities
for multidimensional Wiener processes, with multiple extrema. These take
the form of (possibly infinite) series expansions of Gaussian densities. This is
undertaken using the characterization of the Wiener process by the heat equation,
a well known connection in mathematical physics.