# [R-SIG-Finance] fOptions and RQuantlib give different vanilla option premiums

Wed Mar 16 11:16:40 CET 2011

```Dear all,

I was wondering if someone has had similar experience with plain
vanilla European option pricing. I try to compare results using both
package fOptions and RQuantLib for a plain vanilla European option. I
use the example in Haug's Option book given in his intro chapter, it's
also shown in the fOptions package. So fOption gives me the correct
answer, but the EuropeanOption is off by a factor of three and
correspondingly the greeks are off (see below). The interesting thing
is that the wolfram alpha call option valuation gives me the same
result as RQuantlib (i.e. not correct)

http://www.wolframalpha.com/input/?i=call+option

I've tried this with other currency options and Bloomberg and
Superderivatives give me option premiums in line with what I get from
fOptions, don't understand how could I be getting different results
from RQuantLib and Wolfram Alpha. These are closed-form solutions for
plain vanilla, how come there be so much discrepancy in the results.
What am I missing?

Thank you in advance for the help.

library(fOptions)
library(RQuantLib)

> EuropeanOption(type="call", underlying=1.56, strike=1.6, dividendYield=0.06-0.08, riskFreeRate=0.06, maturity=1/2, volatility=0.12)
Concise summary of valuation for EuropeanOption
value   delta   gamma    vega   theta     rho  divRho
0.0652  0.5912  2.9743  0.4343 -0.1220  0.4285 -0.4611

> GBSCharacteristics(TypeFlag = "c", S = 1.5600, X = 1.6000,  Time = 1/2, r = 0.06, b = 0.06-0.08, sigma = 0.12)
[1] 0.02909931
\$delta
[1] 0.3403860
\$theta
[1] -0.03494785
\$vega
[1] 0.3942821
\$rho
[1] 0.2509514
\$lambda
[1] 18.24793
\$gamma
[1] 2.700266

```