# 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

 ```1 2 3 4``` ```## Default S3 method: 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

## 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

## Note

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

## Author(s)

Dirk Eddelbuettel edd@debian.org for the R interface; the QuantLib Group for `QuantLib`

## References

https://www.quantlib.org/ for details on `QuantLib`.

## Examples

 ```1 2 3``` ```# 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 Oct. 6, 2021, 5:06 p.m.