All Moments of Discrete and Continuous Arithmetic Averages on Brownian Paths: A Closed Form

Allen Abrahamson

Finance from EconWPA

Abstract: This note derives new expressions for the moments of the average of values taken by Wiener paths at an arbitrary number, N, of discrete times. The expressions are closed summations, which entail only the N-th powers of, and the successive differences between, the moments of the lognormal finite dimensional distribution of the process' values at the time of the first averaging. By passing to the limit of the average when the averaging frequency becomes continuous, known forms for the continuous average are generalized by a single expression.

Keywords: Brownian Motion; Wiener Processes; Moments; Asian Options; Sample Path Properties; Computation (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2002-05-30
Note: Type of Document - PDF; prepared on IBM PC pdfLatex; to print on HP; pages: 16; figures: none. none
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0205004

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