For some projects I am looking into financial options. I prefer to use RQuantLib, but sometimes its hard to convince others (Mac users for instance) to install QuantLib, Boost, etc. therefore I am also looking at the fOptions-package. However I have issues replicating results.
Mainly I am trying to calculate the price for American and European options, as well as the delta, gamma, vega, theta, and rho.
In RQuantLib everything works as expected:
library(RQuantLib)
EuropeanOption(type = "call", underlying = 100, strike = 100, dividendYield = 0,
riskFreeRate = 0.03, maturity = 1, volatility = 0.05)
# Concise summary of valuation for EuropeanOption
# value delta gamma vega theta rho divRho
# 3.7861 0.7340 0.0656 32.8161 -2.9089 69.6153 -73.4014
fOptions however gives me different results:
library(fOptions)
GBSOption(TypeFlag = "c", S = 100, X = 100, Time = 1, r = 0.03, b = 0,
sigma = 0.05)
#
# Title:
# Black Scholes Option Valuation
#
# Call:
# GBSOption(TypeFlag = "c", S = 100, X = 100, Time = 1, r = 0.03,
# b = 0, sigma = 0.05)
#
# Parameters:
# Value:
# TypeFlag c
# S 100
# X 100
# Time 1
# r 0.03
# b 0
# sigma 0.05
#
# Option Price:
# 1.935566
#
# Description:
# Wed Nov 2 23:08:57 2016
Or similar for the greeks:
GBSGreeks(Selection = "delta", TypeFlag = "c", S = 100, X = 100, Time = 1,
r = 0.03, b = 0, sigma = 0.05)
# [1] 0.4949006
I am not necessarily bound to the fOptions-library, I just need a (rather) lightweight alternative to RQuantLib that doesn't need the installation of additional software (on Mac and Linux).
What am I missing? Thank you very much for your help!
You've misunderstood the purpose of the b argument to fOptions::GBSOption. It's not equivalent to the dividend yield in RQuantLib::EuropeanOption, it's actually the cost of carry. In your case with no dividend yield, the cost of carry is just the risk-free rate:
GBSOption(TypeFlag = "c", S = 100, X = 100, Time = 1, r = 0.03,
sigma = 0.05, b=0.03)
Title:
Black Scholes Option Valuation
Call:
GBSOption(TypeFlag = "c", S = 100, X = 100, Time = 1, r = 0.03,
b = 0.03, sigma = 0.05)
Parameters:
Value:
TypeFlag c
S 100
X 100
Time 1
r 0.03
b 0.03
sigma 0.05
Option Price:
3.786116
This matches what you got from the other package.