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

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 …