Add the pagesize
option. Here is a quote from the manual, end of section 2.7, page 45 and 46:
The above-mentioned mechanisms for choice of paper format only affect
the output insofar as internal LaTeX lengths are set. The typearea
package then uses them in the division of the page into type area and
margins. The specification of the DVI formats, however, does not
include any indications of paper format. If printing is done directly
from DVI format to a low-level printer language such as PCL or ESC/P2,
this is usually not an issue since with this output also the
zero-position is at the top left, identical to DVI. If, however,
translation is made into a language such as PostScript or PDF, in
which the zero-position is at a different point, and in which also the
paper format should be specified in the output data, then this
information is missing. To solve this problem, the respective drivers
use a predefined paper size, which the user can change either by means
of an option or via a corresponding command in the TEX source file.
When using the DVI driver dvips
the information can be given in the
form of a \special command. With pdfTeX or VTeX one sets instead two
lengths.
With option pagesize
you may select an output driver for writing the
paper size into the destination document. Supported output drivers are
listed at table 2.6. The default is pagesize=false
. Usage of option
pagesize without value is same like pagesize=auto
. It is recommended
always to specify this option. Generally the method without
output driver
, or with auto
or automedia
, is useful.
\documentclass[paper=a6,pagesize]{scrbook}
\usepackage{blindtext}
\begin{document}
\Blindtext
\end{document}

a4paper
anda5paper
(and some more), but no according option for A6 format.