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

[Oleg Mubarakshin]

Hi Tom!

I hope you do not try to get option prices with using vol calculated from 
underlying (so called realized or historical vol).
BSM model is a model based on GBM, that we do not see in the real markets of 
course.
Real markets express skew and fat tails in log-return distributions, that 
leads to vol skew and higher implied vol of deep OTM options.

For modeling of option prices often use:
1. Stochastic vol models
2. Local vol models
3. Stochastic local vol models

these models is constructed for catch the effects described by me above.

I hope it will help you!

Kind regards,
Oleg Mubarakshin

-----Исходное сообщение----- 
From: thp
Sent: Thursday, June 09, 2016 9:02 AM
To: r-sig-finance at r-project.org
Subject: [R-SIG-Finance] Option pricing, basic question

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

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