All Moments of Discrete and Continuous Arithmetic Averages on Brownian Paths: A Closed Form
AbstractThis 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.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0205004.
Length: 16 pages
Date of creation: 30 May 2002
Date of revision:
Note: Type of Document - PDF; prepared on IBM PC pdfLatex; to print on HP; pages: 16; figures: none. none
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Brownian Motion; Wiener Processes; Moments; Asian Options; Sample Path Properties; Computation;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-07-31 (All new papers)
- NEP-ECM-2002-08-10 (Econometrics)
- NEP-ETS-2002-07-31 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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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