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

Frank frankm60606 at gmail.com
Thu Jun 9 15:42:11 CEST 2016

I use the 3-month constant maturity Treasury bill rate from FRED (Federal
Reserve Economic ??Database??) for the risk-free rate. For options with
substantially more than 3 months until expiration, I think it makes sense to
use a maturity that best matches the option. The R code I use is:

library(quantmod)
library(chron)

##
## Get DGS3MO Treasury yield from FRED
##

getSymbols('DGS3MO',src='FRED')
DGS3MO<-na.locf(DGS3MO/100.0,na.rm = TRUE)
tail(DGS3MO)
file_name <- "DGS3MO.csv"
write.zoo(DGS3MO, file = file_name, append = FALSE, quote = TRUE, sep = ",")
quit()

I run this text from a batch file in Windows 7 Pro 64-bit. The text in the
batch file is:

REM on Microsoft Windows (adjust the path to R.exe as needed)
DEL *DGS3MO.csv

"C:\Program Files\R\R-3.2.2\bin\x64\R.exe" CMD BATCH
"C:\Users\Frank\Documents\R\Projects\DGS3MO\DGS3MO.txt"
"C:\Users\Frank\Documents\R\Projects\DGS3MO\DGS3MO.out"
COPY DGS3MO.BAT DGS3MO.BAK
COPY DGS3MO.TXT DGS3MO.TXT.BAK
REM PAUSE

You say "r (drift)". Interest rates do move around despite the constant
interest rate assumption of the Black-Scholes model. This could be
characterized as drift. I'm not sure why else drift is in this post.
Correcting for interest rate drift has not mattered in calculations I've

Volatility is also assumed constant in Black-Scholes. Volatility does drift
and this is the core problem with fitting market data to the standard
Black-Scholes model. Correctly correcting for drift might give you a better
fit to market data.

Best,

Frank
Chicago, IL

-----Original Message-----
From: R-SIG-Finance [mailto:r-sig-finance-bounces at r-project.org] On Behalf
Of thp
Sent: Thursday, June 09, 2016 1:03 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

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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