All Moments of Discrete and Continuous Arithmetic Averages on Brownian Paths: A Closed Form
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.
|Date of creation:||30 May 2002|
|Note:||Type of Document - PDF; prepared on IBM PC pdfLatex; to print on HP; pages: 16; figures: none. none|
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- Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
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