Option pricing, basic question
Tom, If you get some options data up for analysis, you might want to try 0 interest first and then DGS3MO second. Using DGS3MO should produce a lower variance between the settlement and the B-S prices. The CBOE sells market data for $3 per month per symbol. The data is voluminous and is best loaded into a database where you can query a relevant subset of data. For instance, all the DEC 2016 SPY Call options that have greater than 0 volume and open interest and are out-of-the-money. Best, Frank Chicago -----Original Message----- From: R-SIG-Finance [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of thp Sent: Thursday, June 09, 2016 11:27 AM To: r-sig-finance at r-project.org Subject: Re: [R-SIG-Finance] Option pricing, basic question Hello to all, I noticed that indeed my questions are not truly specific to R. Nevertheless the code in Frank's post was guiding to FRED which contributes to answers. With "drift" I mistakenly meant "risk-free rate"; properly one refers to "drift" when meaning the overall movement of the _underlying_. Tom
On 2016-06-09 15:42, Frank wrote:
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
made.
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
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
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.