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
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
|
## RQuantLib -- R interface to the QuantLib libraries
##
## Copyright (C) 2002 - 2014 Dirk Eddelbuettel <edd@debian.org>
##
## This file is part of RQuantLib.
##
## RQuantLib is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 2 of the License, or
## (at your option) any later version.
##
## RQuantLib 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 General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with RQuantLib. If not, see <http://www.gnu.org/licenses/>.
oldEuropeanOptionArrays <- function(type, underlying, strike, dividendYield,
riskFreeRate, maturity, volatility) {
n.underlying <- length(underlying)
n.strike <- length(strike)
n.dividendYield <- length(dividendYield)
n.riskFreeRate <- length(riskFreeRate)
n.maturity <- length(maturity)
n.volatility <- length(volatility)
res <- numeric(n.underlying * n.strike * n.dividendYield * n.riskFreeRate *
n.maturity * n.volatility)
dim(res) <- c(n.underlying, n.strike, n.dividendYield, n.riskFreeRate,
n.maturity, n.volatility)
dimnames(res) <- list(paste("s",underlying,sep="="),
paste("k",strike,sep="="),
paste("y",dividendYield,sep="="),
paste("r",riskFreeRate,sep="="),
paste("t",maturity,sep="="),
paste("v",volatility,sep="="))
value <- delta <- gamma <- vega <- theta <- rho <- divRho <- res
for (s in 1:n.underlying) {
for (k in 1:n.strike) {
for (y in 1:n.dividendYield) {
for (r in 1:n.riskFreeRate) {
for (t in 1:n.maturity) {
for (v in 1:n.volatility) {
val <- europeanOptionEngine(type, underlying, strike,
dividendYield, riskFreeRate,
maturity, volatility)
value[s,k,y,r,t,v] <- val$value
delta[s,k,y,r,t,v] <- val$delta
gamma[s,k,y,r,t,v] <- val$gamma
vega[s,k,y,r,t,v] <- val$vega
theta[s,k,y,r,t,v] <- val$theta
rho[s,k,y,r,t,v] <- val$rho
divRho[s,k,y,r,t,v] <- val$divRho
}
}
}
}
}
}
value <- drop(value)
delta <- drop(delta)
gamma <- drop(gamma)
vega <- drop(vega)
theta <- drop(theta)
rho <- drop(rho)
divRho <- drop(divRho)
invisible(list(value=value, delta=delta, gamma=gamma, vega=vega,
theta=theta, rho=rho, divRho=divRho,
parameters=list(type=type, underlying=underlying,
strike=strike, dividendYield=dividendYield,
riskFreeRate=riskFreeRate, maturity=maturity,
volatility=volatility)))
}
EuropeanOptionArrays <- function(type, underlying, strike, dividendYield,
riskFreeRate, maturity, volatility) {
## check that we have two vectors
lv <- c(length(underlying) > 1,
length(strike) > 1,
length(dividendYield) > 1,
length(riskFreeRate) > 1, +
length(maturity) > 1, +
length(volatility) > 1)
if (sum(lv) != 2) {
warning("Need exactly two arguments as vectors")
return(NULL)
}
type <- match.arg(type, c("call", "put"))
## expand parameters
pars <- expand.grid(underlying, strike, dividendYield,
riskFreeRate, maturity, volatility)
nonconst <- which( apply(pars, 2, sd) != 0)
colnames <- c("spot", "strike", "div", "rfrate", "mat", "vol")
val <- europeanOptionArraysEngine(type, as.matrix(pars))
## turn list of vectors in to list of matrices
par1 <- unique(pars[, nonconst[1]])
par2 <- unique(pars[, nonconst[2]])
len1 <- length(par1)
len2 <- length(par2)
ml <- lapply(val, function(x) matrix(x, len1, len2, dimnames=list(par1,par2)))
return(c(ml, parameters=list(type=type, underlying=underlying,
strike=strike, dividendYield=dividendYield,
riskFreeRate=riskFreeRate, maturity=maturity,
volatility=volatility)))
}
plotOptionSurface <- function(EOres, ylabel="", xlabel="", zlabel="", fov=60) {
if (requireNamespace("rgl", quietly=TRUE)) {
if (missing(EOres)) {
message("No 'EOres' argument supplied. Calling 'EuropeanOptionArrays' to show 'delta'.\n",
"See help('EuropeanOptionArrays') for function parameters and available result\n",
"matrices in the returned list object.")
und.seq <- seq(10,180,by=2)
vol.seq <- seq(0.1,0.9,by=0.1)
## evaluate them along with three scalar parameters
EOarr <- EuropeanOptionArrays("call", underlying=und.seq,
strike=100, dividendYield=0.01,
riskFreeRate=0.03,
maturity=1, volatility=vol.seq)
EOres <- EOarr$delta
}
if (packageVersion("rgl") < "0.111.5")
surface3d <- rgl::rgl.surface
else
surface3d <- rgl::surface3d
axis.col <- "black"
text.col <- axis.col
ylab <- ylabel
xlab <- xlabel
zlab <- zlabel
y <- EOres
## clear scene:
rgl::clear3d()
rgl::clear3d(type="bbox")
rgl::clear3d(type="lights")
## setup env:
rgl::bg3d(color="#DDDDDD")
rgl::light3d()
rgl::view3d(fov=fov)
x <- 1:nrow(y)
z <- 1:ncol(y)
x <- (x-min(x))/(max(x)-min(x))
y <- (y-min(y))/(max(y)-min(y))
z <- (z-min(z))/(max(z)-min(z))
surface3d(x = x, y = y, z = z, alpha=0.6, lit=TRUE, color="blue")
rgl::lines3d(c(0,1), c(0,0), c(0,0), col=axis.col)
rgl::lines3d(c(0,0), c(0,1), c(0,0), col=axis.col)
rgl::lines3d(c(0,0),c(0,0), c(0,1), col=axis.col)
rgl::text3d(1,0,0, xlab, adj=1, col=text.col)
rgl::text3d(0,1,0, ylab, adj=1, col=text.col)
rgl::text3d(0,0,1, zlab, adj=1, col=text.col)
## add grid (credit's to John Fox scatter3d)
xgridind <- round(seq(1, nrow(y), length=25))
zgridind <- round(seq(1, ncol(y), length=25))
surface3d(x = x[xgridind], y = y[xgridind,zgridind], z = z[zgridind],
color="darkgray", alpha=0.5, lit=TRUE,
front="lines", back="lines")
## animate (credit to view3d() example)
start <- proc.time()[3]
while ((i <- 36*(proc.time()[3]-start)) < 360) {
rgl::view3d(i,i/8);
}
} else {
message("Please install the 'rgl' package before using this function.")
}
}
utils::globalVariables(c("clear3d", "bg3d", "ligh3d", "view3d", "surface3d", "text3d"))
|
