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.
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:
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.