1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
|
% $Id$
\name{AsianOption}
\alias{AsianOption}
\alias{AsianOption.default}
\title{Asian Option evaluation using Closed-Form solution}
\description{
The \code{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{
\method{AsianOption}{default}(averageType, type, underlying, strike,
dividendYield, riskFreeRate, maturity,
volatility, first=0, length=11.0/12.0, fixings=26)
}
\arguments{
\item{averageType}{Specifiy averaging type, either \dQuote{geometric} or \dQuote{arithmetic} }
\item{type}{A string with one of the values \code{call} or \code{put}}
\item{underlying}{Current price of the underlying stock}
\item{strike}{Strike price of the option}
\item{dividendYield}{Continuous dividend yield (as a fraction) of the stock}
\item{riskFreeRate}{Risk-free rate}
\item{maturity}{Time to maturity (in fractional years)}
\item{volatility}{Volatility of the underlying stock}
\item{first}{(Only for arithmetic averaging) Time step to first
average, can be zero}
\item{length}{(Only for arithmetic averaging) Total time length for
averaging period}
\item{fixings}{(Only for arithmetic averaging) Total number of averaging fixings}
}
\value{
The \code{AsianOption} function returns an object of class
\code{AsianOption} (which inherits from class
\code{\link{Option}}). It contains a list with the following
components:
\item{value}{Value of option}
\item{delta}{Sensitivity of the option value for a change in the underlying}
\item{gamma}{Sensitivity of the option delta for a change in the underlying}
\item{vega}{Sensitivity of the option value for a change in the
underlying's volatility}
\item{theta}{Sensitivity of the option value for a change in t, the
remaining time to maturity}
\item{rho}{Sensitivity of the option value for a change in the
risk-free interest rate}
\item{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
\code{QuantLib} documentation for details on the \code{QuantLib}
implementation.
}
\references{\url{https://www.quantlib.org/} for details on \code{QuantLib}.}
\author{Dirk Eddelbuettel \email{edd@debian.org} for the \R interface;
the QuantLib Group for \code{QuantLib}}
\note{The interface might change in future release as \code{QuantLib}
stabilises its own API.}
\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)
}
\keyword{misc}
|
