[R-SIG-Finance] Option pricing, basic question
frankm60606 at gmail.com
Fri Jun 10 00:27:05 CEST 2016
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.
From: R-SIG-Finance [mailto:r-sig-finance-bounces at r-project.org] On Behalf
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_.
On 2016-06-09 15:42, Frank wrote:
> I use the 3-month constant maturity Treasury bill rate from FRED
> 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:
> ## Get DGS3MO Treasury yield from FRED
> DGS3MO<-na.locf(DGS3MO/100.0,na.rm = TRUE)
> file_name <- "DGS3MO.csv"
> write.zoo(DGS3MO, file = file_name, append = FALSE, quote = TRUE, sep =
> I run this text from a batch file in Windows 7 Pro 64-bit. The text in
> 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
> 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
> Volatility is also assumed constant in Black-Scholes. Volatility does
> and this is the core problem with fitting market data to the standard
> Black-Scholes model. Correctly correcting for drift might give you a
> fit to market data.
> Chicago, IL
> -----Original Message-----
> From: R-SIG-Finance [mailto:r-sig-finance-bounces at r-project.org] On
> 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
> 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 ).
> 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?
>  https://de.wikipedia.org/wiki/Black-Scholes-Modell
> R-SIG-Finance at r-project.org mailing list
> -- 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
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions
More information about the R-SIG-Finance