Abstract
The extrema of Wiener processes are relevant to the pricing of so-called exotic options, which have many financial applications. The probability den-sities of such extrema are well known for one dimensional Wiener processes. We employ elementary methods to derive analytical expressions for the den-sities 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.
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