I unfortunately don't fully understand the financial aspect of the problem, but I'm going to throw something out there, and hopefully we can improve the answer as we go. You might want to comment on this answer / edit your question as appropriate, so we can move towards a satisfactory answer.
Here I generate some data points from a Wiener process $W(0,\sqrt{157/252})$ as you specified. You want the process to last 157 days, and I assume a time step of 1 day. The time step is assumed to be in seconds for TemporalData objects, which is the origin of those conversion factors (i.e. 157 days = 157*24*60*60 seconds).
SeedRandom[10]
data = RandomFunction[
WienerProcess[0, Sqrt[157/252]],
{0, 157*24*60*60, 1*24*60*60}
]
This time-dependent data set is stored in a TemporalData
object:

We can do quite a few things with it. First, let's visualize it. The most straightforward way to do so is to use a generic plotting function, e.g. ListPlot
:
ListPlot[data, Joined -> True]

Since this is time-dependent data, however, we can use a more specialized plotting function that is aware of time spans, such as DateListPlot
:
DateListPlot[data]

You will notice that the DateListPlot took care of the time conversion and is showing dates on its horizontal axis.
Finally, if you just want to have the values of the raw data points that were generated, you can extract them from the TemporalData
object using Normal
:
Normal[data]
Here I'll show only a part of the long output from that command:
{{{0, 0.}, {86400, 104.835}, {172800, -75.3291}, <<152>>, {13392000, -1017.42}, {13478400, -1290.62}, {13564800, -933.656}}}
If you want to generate more than one such path, you can also do so easily from the RandomFunction
expression:
SeedRandom[10]
multipledata = RandomFunction[
WienerProcess[0, Sqrt[157/252]],
{0, 157*24*60*60, 1*24*60*60},
3 (* this is the number of processes to generate *)
]
DateListPlot[multipledata]
