RQuantLib (version 0.4.0)

AsianOption: Asian Option evaluation using Closed-Form solution

Description

The AsianOption function evaluates an Asian-style option on a common stock using an analytic solution for continuous geometric average price. The option value, the common first derivatives ("Greeks") as well as the calling parameters are returned.

Usage

## S3 method for class 'default':
AsianOption(averageType, type, underlying, strike,
	                  dividendYield, riskFreeRate, maturity, 
	                  volatility, first=0, length=11.0/12.0, fixings=26)

Arguments

averageType

Specifiy averaging type, either geometric or arithmetic

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

first

(Only for arithmetic averaging) Time step to first average, can be zero

length

(Only for arithmetic averaging) Total time length for averaging period

fixings

(Only for arithmetic averaging) Total number of averaging fixings

Value

• The AsianOption function returns an object of class AsianOption (which inherits from class Option). 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

Details

When "arithmetic" evaluation is used, only the NPV() is returned. 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.

Examples

# simple call with some explicit parameters, and slightly increased vol:
AsianOption("geometric", "put", underlying=80, strike=85, div=-0.03,
            riskFree=0.05, maturity=0.25, vol=0.2)