EuropeanOptionArrays: European Option evaluation using Closed-Form solution

In RQuantLib: R interface to the QuantLib library

Description

The EuropeanOptionArrays function allows any two of the numerical input parameters to be a vector, and a list of matrices is returned for the option value as well as each of the 'greeks'. For each of the returned matrices, each element corresponds to an evaluation under the given set of parameters.

Usage

EuropeanOptionArrays(type, underlying, strike, dividendYield,
                     riskFreeRate, maturity, volatility)
oldEuropeanOptionArrays(type, underlying, strike, dividendYield,
                        riskFreeRate, maturity, volatility)
plotOptionSurface(EOres, ylabel="", xlabel="", zlabel="", fov=60) 

Arguments

type	A string with one of the values call or put
underlying	(Scalar or list) current price(s) of the underlying stock
strike	(Scalar or list) strike price(s) of the option
dividendYield	(Scalar or list) continuous dividend yield(s) (as a fraction) of the stock
riskFreeRate	(Scalar or list) risk-free rate(s)
maturity	(Scalar or list) time(s) to maturity (in fractional years)
volatility	(Scalar or list) volatilit(y|ies) of the underlying stock
EOres	result matrix produced by EuropeanOptionArrays
ylabel	label for y-axsis
xlabel	label for x-axsis
zlabel	label for z-axsis
fov	viewpoint for 3d rendering

Details

The well-known closed-form solution derived by Black, Scholes and Merton is used for valuation.

Please see any decent Finance textbook for background reading, and the QuantLib documentation for details on the QuantLib implementation.

Value

The EuropeanOptionArrays function allows any two of the numerical input parameters to be a vector or sequence. A list of two-dimensional matrices is returned. Each cell corresponds to an evaluation under the given set of parameters.

For these functions, the following components are returned:

value	(matrix) value of option
delta	(matrix) change in value for a change in the underlying
gamma	(matrix) change in value for a change in delta
vega	(matrix) change in value for a change in the underlying's volatility
theta	(matrix) change in value for a change in delta
rho	(matrix) change in value for a change in time to maturity
dividendRho	(matrix) change in value for a change in delta
parameters	List with parameters with which object was created

The oldEuropeanOptionArrays function is an older implementation which vectorises this at the R level instead but allows more general multidimensional arrays.

Note

The interface might change in future release as QuantLib stabilises its own API.

Author(s)

Dirk Eddelbuettel [e-mail] for the R interface; the QuantLib Group for QuantLib

References

http://quantlib.org for details on QuantLib.

See Also

AmericanOption,BinaryOption

Examples

# define two vectos for the underlying and the volatility
und.seq <- seq(10,180,by=2)
vol.seq <- seq(0.1,0.9,by=0.1)
# evaluate them along with three scalar parameters
EOarr <- EuropeanOptionArrays("call", underlying=und.seq,
                              strike=100, dividendYield=0.01,
                              riskFreeRate=0.03,
                              maturity=1, volatility=vol.seq)
# and look at four of the result arrays: value, delta, gamma, vega
old.par <- par(no.readonly = TRUE)
par(mfrow=c(2,2),oma=c(5,0,0,0),mar=c(2,2,2,1))
plot(EOarr$parameters.underlying, EOarr$value[,1], type='n',
     main="option value", xlab="", ylab="") 
topocol <- topo.colors(length(vol.seq))
for (i in 1:length(vol.seq))
  lines(EOarr$parameters.underlying, EOarr$value[,i], col=topocol[i])
plot(EOarr$parameters.underlying, EOarr$delta[,1],type='n',
     main="option delta", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameters.underlying, EOarr$delta[,i], col=topocol[i])
plot(EOarr$parameters.underlying, EOarr$gamma[,1],type='n',
     main="option gamma", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameters.underlying, EOarr$gamma[,i], col=topocol[i])
plot(EOarr$parameters.underlying, EOarr$vega[,1],type='n',
     main="option vega", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameters.underlying, EOarr$vega[,i], col=topocol[i])
mtext(text=paste("Strike is 100, maturity 1 year, riskless rate 0.03",
        "\nUnderlying price from", und.seq[1],"to", und.seq[length(und.seq)],
        "\nVolatility  from",vol.seq[1], "to",vol.seq[length(vol.seq)]),
      side=1,font=1,outer=TRUE,line=3)
par(old.par)

Example output

sh: 1: cannot create /dev/null: Permission denied

RQuantLib documentation built on May 2, 2019, 4:48 p.m.