AsianOption: Asian Option evaluation using Closed-Form solution

In RQuantLib: R interface to the QuantLib library

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

## Default S3 method:
AsianOption(averageType, type, underlying, strike,
	                  dividendYield, riskFreeRate, maturity, 
	                  volatility, first=0, length=0, fixings=0)

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	to be written
length	to be written
fixings	to be written

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.

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
parameters	List with parameters with which object was created

Note

The interface might change in future release as QuantLib stabilises its own API.

Author(s)

Dirk Eddelbuettel [e-mail] for the R interface; the QuantLib Group for QuantLib

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)

Example output

sh: 1: cannot create /dev/null: Permission denied
Concise summary of valuation for AsianOption 
  value   delta   gamma    vega   theta     rho  divRho 
 4.6922 -0.8031  0.0594  6.8662  0.0580 -9.2039  8.0309 

RQuantLib documentation built on May 2, 2019, 4:48 p.m.