Nothing
R/BinaryOptions.R
In fExoticOptions: Rmetrics - Pricing and Evaluating Exotic Option
Defines functions
GapOption
CashOrNothingOption
TwoAssetCashOrNothingOption
AssetOrNothingOption
SuperShareOption
BinaryBarrierOption
Documented in
AssetOrNothingOption
BinaryBarrierOption
CashOrNothingOption
GapOption
SuperShareOption
TwoAssetCashOrNothingOption
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
################################################################################
# FUNCTION: DESCRIPTION:
# Binary Options:
# GapOption Gap Option
# CashOrNothingOption Cash Or Nothing Option
# TwoAssetCashOrNothingOption Two Asset Cash-Or Nothing Option
# AssetOrNothingOption Asset Or Nothing Option
# SuperShareOption Super Share Option
# BinaryBarrierOption Binary Barrier Option
################################################################################
GapOption =
function(TypeFlag = c("c", "p"), S, X1, X2, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Gap Options
# References:
# Haug, Haug Chapter 2.11.1
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d1 = (log(S/X1) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
d2 = d1 - sigma*sqrt (Time)
if (TypeFlag == "c")
GapOption = S*exp((b-r)*Time)*CND(d1) - X2*exp(-r*Time)*CND(d2)
if (TypeFlag == "p")
GapOption = X2*exp(-r*Time)*CND(-d2) - S*exp((b-r)*Time)*CND(-d1)
# Parameters:
# TypeFlag = c("c", "p"), S, X1, X2, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X1 = X1
param$X2 = X2
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Gap Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = GapOption,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
CashOrNothingOption =
function(TypeFlag = c("c", "p"), S, X, K, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Cash-Or-Nothing Options
# References:
# Haug, Chapter 2.11.2
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d = (log(S / X) + (r + b - sigma ^ 2 / 2) * Time) / (sigma * sqrt(Time))
if (TypeFlag == "c")
CashOrNothing = K * exp (-r * Time) * CND(d)
if (TypeFlag == "p")
CashOrNothing = K * exp (-r * Time) * CND(-d)
# Parameters:
# TypeFlag = c("c", "p"), S, X, K, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$K = K
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Cash Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = CashOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
TwoAssetCashOrNothingOption =
function(TypeFlag = c("c", "p", "ud", "du"), S1, S2, X1, X2, K, Time, r,
b1, b2, sigma1, sigma2, rho, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Two Asset Cash-Or-Nothing Options
# References:
# Haug, Chapter 2.11.3
# Arguments:
# 1: Asset One, 2: Asset Two
# TypeFlag
# 1 Call
# 2 Put
# 3 Up-Down
# 4 Down-Up
# S=c(S1,S2) Asset Prices
# K Payout
# X=c(X1,X2) Strikes
# b=c(b1,b2) Cost-of-Carry
# sigma=c(sigma1,sigma2) Volatilities
# rho Correlation
#
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d11 = ((log(S1/X1) + (b1 - sigma1^2/2) * Time) /
(sigma1*sqrt(Time)))
d22 = ((log(S2/X2) + (b2 - sigma2^2/2) * Time) /
(sigma2*sqrt(Time)))
# Select:
if (TypeFlag == "c")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND( d11, d22, rho)
if (TypeFlag == "p")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND(-d11, -d22, rho)
if (TypeFlag == "ud")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND( d11, -d22, -rho)
if (TypeFlag == "du")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND(-d11, d22, -rho)
# Parameters:
# TypeFlag = c("c", "p", "ud", "du"), S1, S2, X1, X2, K, Time, r,
# b1, b2, sigma1, sigma2, rho
param = list()
param$TypeFlag = TypeFlag
param$S1 = S1
param$S2 = S2
param$X1 = X1
param$X2 = X2
param$K = K
param$Time = Time
param$r = r
param$b1 = b1
param$b2 = b2
param$sigma1 = sigma1
param$sigma2 = sigma2
param$rho = rho
# Add title and description:
if (is.null(title)) title = "Two Asset Cash Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = TwoAssetCashOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
AssetOrNothingOption =
function(TypeFlag = c("c", "p"), S, X, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Asset-or-Nothing Options
# Reference:
# Cox Rubinstein (1985)
# Haug, Chapter 2.11.4
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d = (log(S/X) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
if (TypeFlag == "c")
AssetOrNothing = S * exp ((b - r) * Time) * CND( d)
if (TypeFlag == "p")
AssetOrNothing = S * exp ((b - r) * Time) * CND(-d)
# Parameters:
# # TypeFlag = c("c", "p"), S, X, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Asset Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = AssetOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
SuperShareOption =
function(S, XL, XH, Time, r, b, sigma, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Supershare Options
# Reference:
# Hakansson (1976)
# Haug, Chapter 2.11.5
# FUNCTION:
# Compute Price:
d1 = (log(S/XL) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
d2 = (log(S/XH) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
SuperShare = (S * exp((b-r)*Time) / XL) * (CND(d1) - CND(d2))
# Parameters:
# S, XL, XH, Time, r, b, sigma
param = list()
param$S = S
param$XL = XL
param$XH = XH
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Super Share Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = SuperShare,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
BinaryBarrierOption =
function(TypeFlag = as.character(1:28), S, X, H, K, Time, r, b, sigma,
eta, phi, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Binary Barrier Options
# Reference:
# Reiner and Rubinstein (1991)
# Haug, Chapter 2.11.6
# FUNCTION:
# Compute Price:
TypeFlag = as.integer(TypeFlag[1])
eta = rep(c(+1,-1), 14)[TypeFlag]
# 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
phi = c(+0,+0,+0,+0,-1,+1,-1,+1,+1,-1,+1,-1,+1,+1,
+1,+1,-1,-1,-1,-1,+1,+1,+1,+1,-1,-1,-1,-1)[TypeFlag]
v = sigma
mu = (b - v ^ 2 / 2) / v ^ 2
lambda = sqrt(mu ^ 2 + 2 * r / v ^ 2)
X1 = log(S / X) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
X2 = log(S / H) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
y1 = log(H ^ 2 / (S * X)) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
y2 = log(H / S) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
Z = log(H / S) / (v * sqrt(Time)) + lambda * v * sqrt(Time)
# Values:
a1 = S * exp((b - r) * Time) * CND(phi * X1)
b1 = K * exp(-r * Time) * CND(phi * X1 - phi * v * sqrt(Time))
a2 = S * exp((b - r) * Time) * CND(phi * X2)
b2 = K * exp(-r * Time) * CND(phi * X2 - phi * v * sqrt(Time))
a3 = (S * exp((b - r) * Time) * (H / S) ^ (2 * (mu + 1)) *
CND(eta * y1))
b3 = (K * exp(-r * Time) * (H / S) ^ (2 * mu) *
CND(eta * y1 - eta * v * sqrt(Time)))
a4 = (S * exp((b - r) * Time) * (H / S) ^ (2 * (mu + 1)) *
CND(eta * y2))
b4 = (K * exp(-r * Time) * (H / S) ^ (2 * mu) *
CND(eta * y2 - eta * v * sqrt(Time)))
a5 = (K * ((H / S) ^ (mu + lambda) *
CND(eta * Z) + (H / S) ^ (mu - lambda) *
CND(eta * Z - 2 * eta * lambda * v * sqrt(Time))))
# Select:
BinaryBarrier = NA
if (X > H) {
if (TypeFlag == 1) BinaryBarrier = a5
if (TypeFlag == 2) BinaryBarrier = a5
if (TypeFlag == 3) BinaryBarrier = a5
if (TypeFlag == 4) BinaryBarrier = a5
if (TypeFlag == 5) BinaryBarrier = b2 + b4
if (TypeFlag == 6) BinaryBarrier = b2 + b4
if (TypeFlag == 7) BinaryBarrier = a2 + a4
if (TypeFlag == 8) BinaryBarrier = a2 + a4
if (TypeFlag == 9) BinaryBarrier = b2 - b4
if (TypeFlag == 10) BinaryBarrier = b2 - b4
if (TypeFlag == 11) BinaryBarrier = a2 - a4
if (TypeFlag == 12) BinaryBarrier = a2 - a4
if (TypeFlag == 13) BinaryBarrier = b3
if (TypeFlag == 14) BinaryBarrier = b3
if (TypeFlag == 15) BinaryBarrier = a3
if (TypeFlag == 16) BinaryBarrier = a1
if (TypeFlag == 17) BinaryBarrier = b2 - b3 + b4
if (TypeFlag == 18) BinaryBarrier = b1 - b2 + b4
if (TypeFlag == 19) BinaryBarrier = a2 - a3 + a4
if (TypeFlag == 20) BinaryBarrier = a1 - a2 + a3
if (TypeFlag == 21) BinaryBarrier = b1 - b3
if (TypeFlag == 22) BinaryBarrier = 0
if (TypeFlag == 23) BinaryBarrier = a1 - a3
if (TypeFlag == 24) BinaryBarrier = 0
if (TypeFlag == 25) BinaryBarrier = b1 - b2 + b3 - b4
if (TypeFlag == 26) BinaryBarrier = b2 - b4
if (TypeFlag == 27) BinaryBarrier = a1 - a2 + a3 - a4
if (TypeFlag == 28) BinaryBarrier = a2 - a4 }
# Continue:
if (X < H) {
if (TypeFlag == 1) BinaryBarrier = a5
if (TypeFlag == 2) BinaryBarrier = a5
if (TypeFlag == 3) BinaryBarrier = a5
if (TypeFlag == 4) BinaryBarrier = a5
if (TypeFlag == 5) BinaryBarrier = b2 + b4
if (TypeFlag == 6) BinaryBarrier = b2 + b4
if (TypeFlag == 7) BinaryBarrier = a2 + a4
if (TypeFlag == 8) BinaryBarrier = a2 + a4
if (TypeFlag == 9) BinaryBarrier = b2 - b4
if (TypeFlag == 10) BinaryBarrier = b2 - b4
if (TypeFlag == 11) BinaryBarrier = a2 - a4
if (TypeFlag == 12) BinaryBarrier = a2 - a4
if (TypeFlag == 13) BinaryBarrier = b1 - b2 + b4
if (TypeFlag == 14) BinaryBarrier = b2 - b3 + b4
if (TypeFlag == 15) BinaryBarrier = a1 - a2 + a4
if (TypeFlag == 16) BinaryBarrier = a2 - a3 + a4
if (TypeFlag == 17) BinaryBarrier = b1
if (TypeFlag == 18) BinaryBarrier = b3
if (TypeFlag == 19) BinaryBarrier = a1
if (TypeFlag == 20) BinaryBarrier = a3
if (TypeFlag == 21) BinaryBarrier = b2 - b4
if (TypeFlag == 22) BinaryBarrier = b1 - b2 + b3 - b4
if (TypeFlag == 23) BinaryBarrier = a2 - a4
if (TypeFlag == 24) BinaryBarrier = a1 - a2 + a3 - a4
if (TypeFlag == 25) BinaryBarrier = 0
if (TypeFlag == 26) BinaryBarrier = b1 - b3
if (TypeFlag == 27) BinaryBarrier = 0
if (TypeFlag == 28) BinaryBarrier = a1 - a3 }
# Parameters:
# TypeFlag = as.character(1:28), S, X, H, K, Time, r, b, sigma, eta, phi
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$H = H
param$K = K
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
param$eta = eta
param$phi = phi
# Add title and description:
if (is.null(title)) title = "Binary Barrier Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = BinaryBarrier,
title = title,
description = description
)
}
################################################################################
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Defines functions GapOption CashOrNothingOption TwoAssetCashOrNothingOption AssetOrNothingOption SuperShareOption BinaryBarrierOption
Documented in AssetOrNothingOption BinaryBarrierOption CashOrNothingOption GapOption SuperShareOption TwoAssetCashOrNothingOption
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
################################################################################
# FUNCTION: DESCRIPTION:
# Binary Options:
# GapOption Gap Option
# CashOrNothingOption Cash Or Nothing Option
# TwoAssetCashOrNothingOption Two Asset Cash-Or Nothing Option
# AssetOrNothingOption Asset Or Nothing Option
# SuperShareOption Super Share Option
# BinaryBarrierOption Binary Barrier Option
################################################################################
GapOption =
function(TypeFlag = c("c", "p"), S, X1, X2, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Gap Options
# References:
# Haug, Haug Chapter 2.11.1
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d1 = (log(S/X1) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
d2 = d1 - sigma*sqrt (Time)
if (TypeFlag == "c")
GapOption = S*exp((b-r)*Time)*CND(d1) - X2*exp(-r*Time)*CND(d2)
if (TypeFlag == "p")
GapOption = X2*exp(-r*Time)*CND(-d2) - S*exp((b-r)*Time)*CND(-d1)
# Parameters:
# TypeFlag = c("c", "p"), S, X1, X2, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X1 = X1
param$X2 = X2
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Gap Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = GapOption,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
CashOrNothingOption =
function(TypeFlag = c("c", "p"), S, X, K, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Cash-Or-Nothing Options
# References:
# Haug, Chapter 2.11.2
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d = (log(S / X) + (r + b - sigma ^ 2 / 2) * Time) / (sigma * sqrt(Time))
if (TypeFlag == "c")
CashOrNothing = K * exp (-r * Time) * CND(d)
if (TypeFlag == "p")
CashOrNothing = K * exp (-r * Time) * CND(-d)
# Parameters:
# TypeFlag = c("c", "p"), S, X, K, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$K = K
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Cash Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = CashOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
TwoAssetCashOrNothingOption =
function(TypeFlag = c("c", "p", "ud", "du"), S1, S2, X1, X2, K, Time, r,
b1, b2, sigma1, sigma2, rho, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Two Asset Cash-Or-Nothing Options
# References:
# Haug, Chapter 2.11.3
# Arguments:
# 1: Asset One, 2: Asset Two
# TypeFlag
# 1 Call
# 2 Put
# 3 Up-Down
# 4 Down-Up
# S=c(S1,S2) Asset Prices
# K Payout
# X=c(X1,X2) Strikes
# b=c(b1,b2) Cost-of-Carry
# sigma=c(sigma1,sigma2) Volatilities
# rho Correlation
#
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d11 = ((log(S1/X1) + (b1 - sigma1^2/2) * Time) /
(sigma1*sqrt(Time)))
d22 = ((log(S2/X2) + (b2 - sigma2^2/2) * Time) /
(sigma2*sqrt(Time)))
# Select:
if (TypeFlag == "c")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND( d11, d22, rho)
if (TypeFlag == "p")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND(-d11, -d22, rho)
if (TypeFlag == "ud")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND( d11, -d22, -rho)
if (TypeFlag == "du")
TwoAssetCashOrNothing = K * exp (-r * Time) * CBND(-d11, d22, -rho)
# Parameters:
# TypeFlag = c("c", "p", "ud", "du"), S1, S2, X1, X2, K, Time, r,
# b1, b2, sigma1, sigma2, rho
param = list()
param$TypeFlag = TypeFlag
param$S1 = S1
param$S2 = S2
param$X1 = X1
param$X2 = X2
param$K = K
param$Time = Time
param$r = r
param$b1 = b1
param$b2 = b2
param$sigma1 = sigma1
param$sigma2 = sigma2
param$rho = rho
# Add title and description:
if (is.null(title)) title = "Two Asset Cash Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = TwoAssetCashOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
AssetOrNothingOption =
function(TypeFlag = c("c", "p"), S, X, Time, r, b, sigma,
title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Asset-or-Nothing Options
# Reference:
# Cox Rubinstein (1985)
# Haug, Chapter 2.11.4
# FUNCTION:
# Compute Price:
TypeFlag = TypeFlag[1]
d = (log(S/X) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
if (TypeFlag == "c")
AssetOrNothing = S * exp ((b - r) * Time) * CND( d)
if (TypeFlag == "p")
AssetOrNothing = S * exp ((b - r) * Time) * CND(-d)
# Parameters:
# # TypeFlag = c("c", "p"), S, X, Time, r, b, sigma
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Asset Or Nothing Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = AssetOrNothing,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
SuperShareOption =
function(S, XL, XH, Time, r, b, sigma, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Supershare Options
# Reference:
# Hakansson (1976)
# Haug, Chapter 2.11.5
# FUNCTION:
# Compute Price:
d1 = (log(S/XL) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
d2 = (log(S/XH) + (b + sigma^2 / 2) * Time) / (sigma * sqrt(Time))
SuperShare = (S * exp((b-r)*Time) / XL) * (CND(d1) - CND(d2))
# Parameters:
# S, XL, XH, Time, r, b, sigma
param = list()
param$S = S
param$XL = XL
param$XH = XH
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
# Add title and description:
if (is.null(title)) title = "Super Share Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = SuperShare,
title = title,
description = description
)
}
# ------------------------------------------------------------------------------
BinaryBarrierOption =
function(TypeFlag = as.character(1:28), S, X, H, K, Time, r, b, sigma,
eta, phi, title = NULL, description = NULL)
{ # A function imlemented by Diethelm Wuertz
# Description:
# Binary Barrier Options
# Reference:
# Reiner and Rubinstein (1991)
# Haug, Chapter 2.11.6
# FUNCTION:
# Compute Price:
TypeFlag = as.integer(TypeFlag[1])
eta = rep(c(+1,-1), 14)[TypeFlag]
# 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
phi = c(+0,+0,+0,+0,-1,+1,-1,+1,+1,-1,+1,-1,+1,+1,
+1,+1,-1,-1,-1,-1,+1,+1,+1,+1,-1,-1,-1,-1)[TypeFlag]
v = sigma
mu = (b - v ^ 2 / 2) / v ^ 2
lambda = sqrt(mu ^ 2 + 2 * r / v ^ 2)
X1 = log(S / X) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
X2 = log(S / H) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
y1 = log(H ^ 2 / (S * X)) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
y2 = log(H / S) / (v * sqrt(Time)) + (mu + 1) * v * sqrt(Time)
Z = log(H / S) / (v * sqrt(Time)) + lambda * v * sqrt(Time)
# Values:
a1 = S * exp((b - r) * Time) * CND(phi * X1)
b1 = K * exp(-r * Time) * CND(phi * X1 - phi * v * sqrt(Time))
a2 = S * exp((b - r) * Time) * CND(phi * X2)
b2 = K * exp(-r * Time) * CND(phi * X2 - phi * v * sqrt(Time))
a3 = (S * exp((b - r) * Time) * (H / S) ^ (2 * (mu + 1)) *
CND(eta * y1))
b3 = (K * exp(-r * Time) * (H / S) ^ (2 * mu) *
CND(eta * y1 - eta * v * sqrt(Time)))
a4 = (S * exp((b - r) * Time) * (H / S) ^ (2 * (mu + 1)) *
CND(eta * y2))
b4 = (K * exp(-r * Time) * (H / S) ^ (2 * mu) *
CND(eta * y2 - eta * v * sqrt(Time)))
a5 = (K * ((H / S) ^ (mu + lambda) *
CND(eta * Z) + (H / S) ^ (mu - lambda) *
CND(eta * Z - 2 * eta * lambda * v * sqrt(Time))))
# Select:
BinaryBarrier = NA
if (X > H) {
if (TypeFlag == 1) BinaryBarrier = a5
if (TypeFlag == 2) BinaryBarrier = a5
if (TypeFlag == 3) BinaryBarrier = a5
if (TypeFlag == 4) BinaryBarrier = a5
if (TypeFlag == 5) BinaryBarrier = b2 + b4
if (TypeFlag == 6) BinaryBarrier = b2 + b4
if (TypeFlag == 7) BinaryBarrier = a2 + a4
if (TypeFlag == 8) BinaryBarrier = a2 + a4
if (TypeFlag == 9) BinaryBarrier = b2 - b4
if (TypeFlag == 10) BinaryBarrier = b2 - b4
if (TypeFlag == 11) BinaryBarrier = a2 - a4
if (TypeFlag == 12) BinaryBarrier = a2 - a4
if (TypeFlag == 13) BinaryBarrier = b3
if (TypeFlag == 14) BinaryBarrier = b3
if (TypeFlag == 15) BinaryBarrier = a3
if (TypeFlag == 16) BinaryBarrier = a1
if (TypeFlag == 17) BinaryBarrier = b2 - b3 + b4
if (TypeFlag == 18) BinaryBarrier = b1 - b2 + b4
if (TypeFlag == 19) BinaryBarrier = a2 - a3 + a4
if (TypeFlag == 20) BinaryBarrier = a1 - a2 + a3
if (TypeFlag == 21) BinaryBarrier = b1 - b3
if (TypeFlag == 22) BinaryBarrier = 0
if (TypeFlag == 23) BinaryBarrier = a1 - a3
if (TypeFlag == 24) BinaryBarrier = 0
if (TypeFlag == 25) BinaryBarrier = b1 - b2 + b3 - b4
if (TypeFlag == 26) BinaryBarrier = b2 - b4
if (TypeFlag == 27) BinaryBarrier = a1 - a2 + a3 - a4
if (TypeFlag == 28) BinaryBarrier = a2 - a4 }
# Continue:
if (X < H) {
if (TypeFlag == 1) BinaryBarrier = a5
if (TypeFlag == 2) BinaryBarrier = a5
if (TypeFlag == 3) BinaryBarrier = a5
if (TypeFlag == 4) BinaryBarrier = a5
if (TypeFlag == 5) BinaryBarrier = b2 + b4
if (TypeFlag == 6) BinaryBarrier = b2 + b4
if (TypeFlag == 7) BinaryBarrier = a2 + a4
if (TypeFlag == 8) BinaryBarrier = a2 + a4
if (TypeFlag == 9) BinaryBarrier = b2 - b4
if (TypeFlag == 10) BinaryBarrier = b2 - b4
if (TypeFlag == 11) BinaryBarrier = a2 - a4
if (TypeFlag == 12) BinaryBarrier = a2 - a4
if (TypeFlag == 13) BinaryBarrier = b1 - b2 + b4
if (TypeFlag == 14) BinaryBarrier = b2 - b3 + b4
if (TypeFlag == 15) BinaryBarrier = a1 - a2 + a4
if (TypeFlag == 16) BinaryBarrier = a2 - a3 + a4
if (TypeFlag == 17) BinaryBarrier = b1
if (TypeFlag == 18) BinaryBarrier = b3
if (TypeFlag == 19) BinaryBarrier = a1
if (TypeFlag == 20) BinaryBarrier = a3
if (TypeFlag == 21) BinaryBarrier = b2 - b4
if (TypeFlag == 22) BinaryBarrier = b1 - b2 + b3 - b4
if (TypeFlag == 23) BinaryBarrier = a2 - a4
if (TypeFlag == 24) BinaryBarrier = a1 - a2 + a3 - a4
if (TypeFlag == 25) BinaryBarrier = 0
if (TypeFlag == 26) BinaryBarrier = b1 - b3
if (TypeFlag == 27) BinaryBarrier = 0
if (TypeFlag == 28) BinaryBarrier = a1 - a3 }
# Parameters:
# TypeFlag = as.character(1:28), S, X, H, K, Time, r, b, sigma, eta, phi
param = list()
param$TypeFlag = TypeFlag
param$S = S
param$X = X
param$H = H
param$K = K
param$Time = Time
param$r = r
param$b = b
param$sigma = sigma
param$eta = eta
param$phi = phi
# Add title and description:
if (is.null(title)) title = "Binary Barrier Option"
if (is.null(description)) description = as.character(date())
# Return Value:
new("fOPTION",
call = match.call(),
parameters = param,
price = BinaryBarrier,
title = title,
description = description
)
}
################################################################################
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