Describing n-day returns with Student’s t-distributions

Daniel T. Cassidy

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 15, 2794-2802

Abstract: Prices for European call options can be calculated for returns that follow a Student’s t-distribution if the t-distribution is truncated or if the value of the asset is capped. The distributions for n-fold convolution of a Student’s t-distribution and a truncated Student’s t-distribution, both with ν=3, are considered in this work. It is shown that a truncated Student’s t-distribution under n-fold self-convolution becomes normal-like whereas a Student’s t-distribution retains the fat tails of the original distribution under n-fold self-convolution. These results can be used to explain the development of the distribution of n-day returns from a truncated Student’s t-distribution for the daily returns to normal as n increases from 1 to 10 or 100. A truncated Student’s t-distribution with 3±0.5 degrees of freedom fits the daily returns of the DJIA and S&P 500 indices.

Keywords: Student’s t-distribution; Truncation; Self-convolution; European options (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:15:p:2794-2802

DOI: 10.1016/j.physa.2011.03.019

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