RQuantLib (version 0.1.5)

EuropeanOption: European Option evaluation using Closed-Form solution

Description

The EuropeanOption function evaluations an European-style option on a common stock using the Black-Scholes-Merton solution. The option value, the common first derivatives ("Greeks") as well as the calling parameters are returned.

Usage

EuropeanOption.default(type, underlying, strike, dividendYield, riskFreeRate, maturity, volatility)
## S3 method for class 'Option':
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## S3 method for class 'Option':
printundefined
## S3 method for class 'Option':
summaryundefined

Arguments

type

A string with one of the values call, put or straddle

value

Value of the option (used only for ImpliedVolatility calculation)

underlying

Current price of the underlying stock

strike

Strike price of the option

dividendYield

Continuous dividend yield (as a fraction) of the stock

riskFreeRate

Risk-free rate

maturity

Time to maturity (in fractional years)

volatility

Volatility of the underlying stock

Value

• The EuropeanOption function returns an object of class EuropeanOption (which inherits from class Option). It contains a list with the following components can be returned:
• value
  Value of option
• delta
  Change in value for a change in the underlying
• gamma
  Change in value for a change in delta
• vega
  Change in value for a change in the underlying's volatility
• theta
  Change in value for a change in delta
• rho
  Change in value for a change in time to maturity
• dividendRho
  Change in value for a change in delta
• parameters
  List with parameters with which object was created

Details

The well-known closed-form solution derived by Black, Scholes and Merton is used for valuation. Implied volatilities are calculated numerically.

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.

See Also

EuropeanOptionImpliedVolatility, EuropeanOptionArrays, AmericanOption,BinaryOption

Examples

# simple call with unnamed parameters
EuropeanOption("call", 100, 100, 0.01, 0.03, 0.5, 0.4)
# simple call with some explicit parameters
EuropeanOption("call",100, 100, 0.01, 0.03, 0.5, 0.4)