[R-SIG-Finance] Option pricing, basic question

[thp]

Hello,

I have a question regarding option pricing. In advance:
thank you for the patience.

I am trying to replay the calculation of plain
vanilla option prices using the Black-Scholes model
(the one leading to the analytic solution seen for
example on the wikipedia page [1]).

Using numerical values as simply obtained from
an arbitrary broker, I am surprised to see that
the formula values and quoted prices mismatch
a lot. (seems cannot all be explained by spread
or dividend details)

My question: What values for r (drift) and \sigma^2
are usually to be used, in which units?

If numerical values are chosen to be given "per year",
then I would expect r to be chosen as \ln(1+i),
where i is the yearly interest rate of the risk-free
portfolio and \ln is the natural logarithm. Would the
risk-free rate currently be chosen as zero?

The \sigma^2 one would accordingly have to choose
as the variance of the underlying security over
a one year period. Should this come out equal in
numerical value to the implied volatility, which is
0.2 to 0.4 for the majority of options?

Tom

[1] https://de.wikipedia.org/wiki/Black-Scholes-Modell