EuropeanOptionArrays: European Option evaluation using Closed-Form solution

Description

The EuropeanOptionArrays function allows any of the numerical input parameters to be a list, and a list of arrays is returned. Each of the returned arrays has as many dimension as there were lists among the input parameters, and each multi-dimensional array element corresponds to an evaluation under the given set of parameters.

Usage

EuropeanOptionArrays(type, underlying, strike, dividendYield, riskFreeRate, maturity, volatility)

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

Value

The EuropeanOptionArrays function allows each of the numerical input parameters to be a list (or vector, or sequence). A list of multi-dimensional arrays is returned. Each array point corresponds to an evaluation under the given set of parameters.
For these functions, the following components are returned:
value(Scalar or array) value of option
delta(Scalar or array) change in value for a change in the underlying
gamma(Scalar or array) change in value for a change in delta
vega(Scalar or array) change in value for a change in the underlying's volatility
theta(Scalar or array) change in value for a change in delta
rho(Scalar or array) change in value for a change in time to maturity
dividendRho(Scalar or array) change in value for a change in delta
parametersList with parameters with which object was created

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.

References

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

Examples

Run this code

# 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$parameter$underlying, EOarr$value[,1], type='n',
     main="option value", xlab="", ylab="") 
topocol <- topo.colors(length(vol.seq))
for (i in 1:length(vol.seq))
  lines(EOarr$parameter$underlying, EOarr$value[,i], col=topocol[i])
plot(EOarr$parameter$underlying, EOarr$delta[,1],type='n',
     main="option delta", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameter$underlying, EOarr$delta[,i], col=topocol[i])
plot(EOarr$parameter$underlying, EOarr$gamma[,1],type='n',
     main="option gamma", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameter$underlying, EOarr$gamma[,i], col=topocol[i])
plot(EOarr$parameter$underlying, EOarr$vega[,1],type='n',
     main="option vega", xlab="", ylab="")
for (i in 1:length(vol.seq))
  lines(EOarr$parameter$underlying, EOarr$vega[,i], col=topocol[i])
mtext(text=paste("Strike is 100, maturity 1 year, riskless rate 0.03",
        "Underlying price from", und.seq[1],"to", und.seq[length(und.seq)],
        "Volatility  from",vol.seq[1], "to",vol.seq[length(vol.seq)]),
      side=1,font=1,outer=TRUE,line=3)
par(old.par)

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