RQuantLib (version 0.2.2)

AmericanOption: American Option evaluation using Finite Differences

Description

This function evaluations an American-style option on a common stock using finite differences. The option value as well as the common first derivatives ("Greeks") are returned.

Usage

AmericanOption.default(type, underlying, strike, dividendYield, riskFreeRate,
maturity, volatility, timeSteps=150, gridPoints=151)
## S3 method for class 'Option':
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## S3 method for class 'Option':
summaryundefined

Arguments

type

A string with one of the values call or put

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

timeSteps

Time steps for the Finite Differences method, default value is 150

gridPoints

Grid points for the Finite Differences method, default value is 151

Value

• An object of class AmericanOption (which inherits from class Option) is returned. It contains a list with the following components:
• value
  Value of option
• delta
  Sensitivity of the option value for a change in the underlying
• gamma
  Sensitivity of the option delta for a change in the underlying
• vega
  Sensitivity of the option value for a change in the underlying's volatility
• theta
  Sensitivity of the option value for a change in t, the remaining time to maturity
• rho
  Sensitivity of the option value for a change in the risk-free interest rate
• dividendRho
  Sensitivity of the option value for a change in the dividend yield
• parameters
  List with parameters with which object was created
• Note that under the new pricing framework used in QuantLib, binary pricers do not provide analytics for 'Greeks'. This is expected to be addressed in future releases of QuantLib.

Details

The Finite Differences method is used to value the American Option. 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

EuropeanOption

Examples

# simple call with unnamed parameters
AmericanOption("call", 100, 100, 0.02, 0.03, 0.5, 0.4)
# simple call with some explicit parameters
AmericanOption("put", strike=100, volatility=0.4, 100, 0.02, 0.03, 0.5)