BinaryOption: Binary Option evaluation using Closed-Form solution
Description
This function evaluations an Binary option on a common stock
using a closed-form solution. The option value as well as the common first
derivatives ("Greeks") are returned.
Usage
## S3 method for class 'default':
BinaryOption(binType, type, excType, underlying,
strike, dividendYield,
riskFreeRate, maturity, volatility, cashPayoff)
Arguments
binType
A string with one of the values cash,
asset or gap to select CashOrNothing, AssetOrNothing
or Gap payoff profiles
type
A string with one of the values call or put
excType
A string with one of the values european or
american to denote the exercise type
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
cashPayoff
Payout amount
Value
An object of class BinaryOption (which inherits from class
Option) is returned. It contains a list with the
following components:
valueValue of option
deltaSensitivity of the option value for a change in the underlying
gammaSensitivity of the option delta for a change in the underlying
vegaSensitivity of the option value for a change in the
underlying's volatility
thetaSensitivity of the option value for a change in t, the
remaining time to maturity
rhoSensitivity of the option value for a change in the
risk-free interest rate
dividendRhoSensitivity of the option value for a change in the
dividend yield
parametersList with parameters with which object was created
Details
A closed-form solution is used to value the Binary Option.
Please see any decent Finance textbook for background reading, and
the QuantLib documentation for details on the QuantLib
implementation.