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

thp thp at 2pimail.com
Thu Jun 9 18:26:42 CEST 2016

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
>
> 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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