https://github.com/cran/fOptions
Tip revision: 429a9b1805024ce58873e3229048371980a535a2 authored by Diethelm Wuertz on 08 August 1977, 00:00:00 UTC
version 221.10065
version 221.10065
Tip revision: 429a9b1
082A-MultipleExercisesOptions.Rd
\name{MultipleExercisesOptions}
\alias{MultipleExercisesOptions}
\alias{ExecutiveStockOption}
\alias{ForwardStartOption}
\alias{RatchetOption}
\alias{TimeSwitchOption}
\alias{SimpleChooserOption}
\alias{ComplexChooserOption}
\alias{OptionOnOption}
\alias{WriterExtendibleOption}
\alias{HolderExtendibleOption}
\title{Valuation of Mutiple Exercises Options}
\description{
A collection and description of functions to valuate
multiple exercise options. Multiple exercises options,
as the name implies, are options whose payoff is based
on multiple exercise dates.
\cr
The functions are:
\tabular{ll}{
\code{ExecutiveStockOption} \tab Executive Stock Option, \cr
\code{ForwardStartOption} \tab Forward Start Option, \cr
\code{RatchetOption} \tab Ratchet Option, \cr
\code{TimeSwitchOption} \tab Time Switch Option, \cr
\code{SimpleChooserOption} \tab Simple Chooser Option, \cr
\code{ComplexChooserOption} \tab Complex Chooser Option, \cr
\code{OptionOnOption} \tab Option On Option, \cr
\code{WriterExtendibleOption} \tab Writer Extendible Option, \cr
\code{HolderExtendibleOption} \tab Holder Extendible Option. }
}
\usage{
ExecutiveStockOption(TypeFlag, S, X, Time, r, b, sigma, lambda,
title = NULL, description = NULL)
ForwardStartOption(TypeFlag, S, alpha, time1, Time2, r, b, sigma,
title = NULL, description = NULL)
RatchetOption(TypeFlag, S, alpha, time1, Time2, r, b, sigma,
title = NULL, description = NULL)
TimeSwitchOption(TypeFlag, S, X, Time, r, b, sigma, A, m, dt,
title = NULL, description = NULL)
SimpleChooserOption(S, X, time1, Time2, r, b, sigma,
title = NULL, description = NULL)
ComplexChooserOption(S, Xc, Xp, Time, Timec, Timep, r, b, sigma,
doprint = FALSE, title = NULL, description = NULL)
OptionOnOption(TypeFlag, S, X1, X2, time1, Time2, r, b, sigma,
doprint = FALSE, title = NULL, description = NULL)
WriterExtendibleOption(TypeFlag, S, X1, X2, time1, Time2, r, b, sigma,
title = NULL, description = NULL)
HolderExtendibleOption(TypeFlag, S, X1, X2, time1, Time2, r, b, sigma, A,
title = NULL, description = NULL)
}
\arguments{
\item{A}{
[HolderExtendible*] - \cr
defined by the amount \code{A*dt} the investor receives
at maturity time \code{Time} for each time interval
\code{deltat} the corresponding asset price has exceeded
the exercise price \code{X}, in the case of a call
option, or the corresponding asset price has been below
the exercise price \code{X}, in the case of a put
option. A numeric value.
}
\item{alpha}{
[Ratchet*] - \cr
the exercise price is \code{alpha} times the asset price
\code{S} after the known time \code{time}. \code{alpha}
is a numeric value. If \code{alpha} is less than unity,
the call (put) will start \code{100*(1-alpha)} percent in
the money (out-of-the-money); if \code{alpha} is unity,
the option will start at the money; and if \code{alpha}
is larger than unity, the call (put) will start
\code{100*(alpha-1)} percentage out of the money
(in-the-money).
}
\item{b}{
the annualized cost-of-carry rate, a numeric value;
e.g. 0.1 means 10\% pa.
}
\item{description}{
a character string which allows for a brief description.
}
\item{doprint}{
a logical. Should the critical value \code{I} be printed?
By defaut \code{FALSE}.
}
\item{dt}{
the time interval; a numeric value.
}
\item{lambda}{
the jump rate pa.
}
\item{m}{
defined by the number of time units where the option
has already fulfilled the thresold condition. This
applies to cases, for which some of the option's total
lifetime has already passed. An integer value.
}
\item{r}{
the annualized rate of interest, a numeric value;
e.g. 0.25 means 25\% pa.
}
\item{S}{
the asset price, a numeric value.
}
\item{sigma}{
the annualized volatility of the underlying security,
a numeric value; e.g. 0.3 means 30\% volatility pa.
}
\item{Time}{
the time to maturity measured in years, a numeric value;
e.g. 0.5 means 6 months.
}
\item{Timec, Timep}{
[ComplexChooser*] - \cr
decision time measured in years, e.g. 0.5 means 6 months.
\code{Timec}, is the time to maturity of the call option,
\code{Timep}, is the time to maturity of the put option,
both also measured in years. Numeric values.
}
\item{time1, Time2}{
the time to maturity, \code{Time1}, measured in years,
e.g. 0.5 means 6 months, and the elapsed time in the
future, \code{Time2}. In detail, the forward start option
with time to maturity \code{Time1} starts at-the-money or
proportinally in-the-money or out-of-the-money after this
elapsed time \code{Time2} in the future.
}
\item{title}{
a character string which allows for a project title.
}
\item{TypeFlag}{
usually a character string either \code{"c"} for a call option
or a \code{"p"} for a put option;\cr
[OptionOnOption] - \cr
a character string either
\code{"cc"} for a call-on-call option, or
\code{"cp"} for a call-on-put option, or
\code{"pc"} for a put-on-call option, or
\code{"pp"} for a put-on-put option.
}
\item{X}{
the exercise price, a numeric value.
}
\item{Xc, Xp}{
[ComplexChooser*] - \cr
the exercise price of the call option, \code{Xc}, and the
exercise price of the put option, \code{Xp}, numeric
values.
}
\item{X1, X2}{
the exercise price of the underlying option, \code{X1}, and
the exercise price of the option on the option, \code{X2},
numeric values.
}
}
\details{
\bold{Executive Stock Options:}
\cr\cr
Executive stock options are usually at-the-money options that are
issued to motivate employees to act in the best interest of the
company. They cannot be sold and often last as long as 10 or 15
years. The executive model takes into account that an employee often
looses their options when they leave the company before expiration.
The value of an executive option equals the standard Black-Scholes
model multiplied by the probability that the employee will stay with
the firm until the option expires. Executive stock options can be priced
analytically using a model published by Jennergren and Naslund (1993).
\cr
[Haug's Book, Chapter 2.1]
\cr
\bold{Forward Start Options:}
\cr\cr
A forward start option is an option which is paid for today, but
will start at some determined time in the future known as the issue
date. The option usually starts at-the-money or proportionally in
or out-of-the-money at a future date. The strike is set to a positive
constant a times the asset price S at a future date. If a is less
than one, the call (put) will start 1 - a percent in-the-money
(out-of-the-money); if a is one, the option will start at-the-money;
and if a is larger than one, the call (put) will start a - 1 percent
out-of-the-money (in-the-money).[1] Forward start options can be
priced analytically using a model published by Rubinstein (1990).
\cr
[Haug's Book, Chapter 2.2]
\cr
\bold{Ratchet [Compound] Options:}
\cr\cr
A compound option is an option on an option. Therefore, when one
option is exercised, the underlying security is another option.
There are four types of possible compound options: a call on a call,
a call on a put, a put on a call, and a put on a put. The owner of
a compound option has until the expiration date of the compound
option to determine whether to exercise the compound option. If
exercised, the owner will receive the underlying option with its
own exercise price and time until expiration. If the underlying
option is exercised, the owner will receive the underlying security.
European compound options can be priced analytically using a model
published by Rubinstein (1991). A binomial lattice is used for the
numerical calculation of an American or European style exchange option.
A ratchet option is also called sometimes a "moving strike option"
or "cliquet option".
\cr
[Haug's Book, Chapter 2.3]
\cr
\bold{Time-Switch Options:}
\cr\cr
For a discrete time-switch call (put) option, the holder receives an
amount ADt at expiration for each time interval, Dt, the corresponding
asset price has been above (below) the strike price. If some of the
option's total lifetime has passed, it is required to add a fixed
amount to the pricing formula. Discrete time-switch options can be
priced analytically using a model published by Pechtl (1995).
\cr
[Haug's Book, Chapter 2.4]
\cr
\bold{Simple Chooser Options:}
\cr\cr
A chooser option allows the holder to determine at some date, after the
trade date, whether the option becomes a plain vanilla call or put.
Chooser options are also called "as you like it" options. Chooser
options are useful for hedging a future event that might not occur.
Due to their increased flexibility, chooser options are more expensive
than plain vanilla options. It is assumed at the options expiration
date that a holder of the chooser option will choose the more valuable
of the put or call option. The less valuable option that was not chosen
will become worthless. Chooser options can be priced analytically using
a model introduced by Rubinstein (1991).
\cr
[Haug's Book, Chapter 2.5.1]
\cr
\bold{Complex Chooser Options:}
\cr\cr
A complex chooser option allows the holder to determine at some date,
after the trade date, whether the option is to be a standard call
chooser model, a complex chooser option will be more expensive than
a plain vanilla option. Complex chooser options can be priced analytically
using a model introduced by Rubinstein (1991).
\cr
[Haug's Book, Chapter 2.5.2]
\cr
\bold{Option On Options:}
\cr\cr
This derivative prices options on options. An option on an option is more
expensive to purchase than the underlying option itself, as the purchaser
has received a price guarantee and effectively extended the life of the
option. These options provide the benefit of a guaranteed price for the
option at a date in the future. Options on Options can be prices as
published by Geske (1977). His model was later extended and discussed
by Geske (1979), Hodges and Selby (1987), and Rubinstein (1991).
\cr
[Haug's Book, Chapter 2.6]
\cr
\bold{Writer [Holder] Extendible Options:}
\cr\cr
Writer extendible options can be found embedded in various financial
contracts. For example, corporate warrants often give the issuing
firm the right to extend the life of the warrants. These options can
be exercised at their initial maturity, but are extended to a new
maturity if they are out-of-the-money at initial maturity. Discrete
time-switch options can be priced analytically using a model published
by Longstaff (1995).
\cr
[Haug's Book, Chapter 2.6]
}
\note{
Options on options are also known as compound options or as
mother-and-daughter options.
}
\value{
The option valuation programs return an object of class
\code{"fOPTION"} with the following slots:
\item{@call}{
the function call.
}
\item{@parameters}{
a list with the input parameters.
}
\item{@price}{
a numeric value with the value of the option.
}
\item{@title}{
a character string with the name of the test.
}
\item{@description}{
a character string with a brief description of the
test.
}
}
\references{
Geske R. (1977);
\emph{The Valuation of Corporate Liabilities as Compound Options},
Journal of Financial and Quantitative Analysis, 541--552.
Geske R. (1979);
\emph{The Valuation of Compound Options},
Journal of Financial Economics 7, 63--81.
Haug E.G. (1997);
\emph{The complete Guide to Option Pricing Formulas},
Chapter 2.8.1, McGraw-Hill, New York.
Hodges S.D., Selby J.P. (1987);
\emph{On the Evaluation of Compound Options};
Management Science 33, 347--355.
Jennergren L.P., Naslund B. (1993);
\emph{A Comment on Valuation of Executive Stock Options and the
FASB Proposal},
The Accounting Review 68, 179, 1993.
Longstaff F.A. (1990);
\emph{Pricing Options with Extendible Maturities: Analysis
and Applications},
Journal of Finance 45, 474--491.
Pechtl A. (1990);
\emph{Classified Information},
Risk Magazine 8.
Rubinstein, M. (1990);
\emph{Pay Now, Choose Later},
Risk Magazine 3.
Rubinstein M. (1991);
\emph{Options for the Undecide},
Risk Magazine 4.
Rubinstein M. (1991);
\emph{Double Trouble};
Risk Magazine 5.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## SOURCE("fOptions.B1-MultipleExercisesOptions")
## Examples from Chapter 2.1 - 2.7 in E.G. Haug's Option Guide (1997)
## ExecutiveStockOption [2.1]:
xmpOptions("\nStart: Executive Stock Option > ")
ExecutiveStockOption(TypeFlag = "c", S = 60, X = 64, Time = 2,
r = 0.07, b = 0.07-0.03, sigma = 0.38, lambda = 0.15)
## ForwardStartOption [2.2]:
xmpOptions("\nNext: Forward Start Option > ")
ForwardStartOption(TypeFlag = "c", S = 60, alpha = 1.1,
time1 = 1, Time2 = 1/4, r = 0.08, b = 0.08-0.04, sigma = 0.30)
## Ratchet Option [2.3]:
xmpOptions("\nNext: Ratchet Option > ")
RatchetOption(TypeFlag = "c", S = 60, alpha = 1.1, time1 = c(1.00, 0.75),
Time2 = c(0.75, 0.50), r = 0.08, b = 0.04, sigma = 0.30)
## Time Switch Option [2.4]:
xmpOptions("\nNext: Time Switch Option > ")
TimeSwitchOption(TypeFlag = "c", S = 100, X = 110, Time = 1,
r = 0.06, b = 0.06, sigma = 0.26, A = 5, m = 0, dt = 1/365)
## Simple Chooser Option [2.5.1]:
xmpOptions("\nNext: Simple Chooser Option > ")
SimpleChooserOption(S = 50, X = 50, time1 = 1/4, Time2 = 1/2,
r = 0.08, b = 0.08, sigma = 0.25)
## Complex Chooser Option [2.5.2]:
xmpOptions("\nNext: Complex Chooser Option > ")
ComplexChooserOption(S = 50, Xc = 55, Xp = 48, Time = 0.25,
Timec = 0.50, Timep = 0.5833, r = 0.10, b = 0.1-0.05,
sigma = 0.35, doprint = TRUE)
## Option On Option [2.6]:
xmpOptions("\nNext: Option On Option > ")
OptionOnOption(TypeFlag = "pc", S = 500, X1 = 520, X2 = 50,
time1 = 1/2, Time2 = 1/4, r = 0.08, b = 0.08-0.03, sigma = 0.35)
## Holder Extendible Option [2.7.1]:
xmpOptions("\nNext: Holder Extendible Option > ")
HolderExtendibleOption(TypeFlag = "c", S = 100, X1 = 100,
X2 = 105, time1 = 0.50, Time2 = 0.75, r = 0.08, b = 0.08,
sigma = 0.25, A = 1)
## Writer Extendible Option [2.7.2]:
xmpOptions("\nNext: Writer Extendible Option > ")
WriterExtendibleOption(TypeFlag = "c", S = 80, X1 = 90, X2 = 82,
time1 = 0.50, Time2 = 0.75, r = 0.10, b = 0.10, sigma = 0.30)
}
\keyword{math}