| Title: | Risk Management and Optimization for Portfolio Investment |
| Version: | 1.1 |
| Description: | Provides functions for risk management and portfolio investment of securities with practical tools for data processing and plotting. Moreover, it contains functions which perform the COS Method, an option pricing method based on the Fourier-cosine series (Fang, F. (2008) <doi:10.1137/080718061>). |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.1 |
| Depends: | ggplot2, tibble, lubridate, timeSeries, xts |
| Imports: | MASS, PerformanceAnalytics, TTR, fPortfolio, rugarch, timeDate |
| NeedsCompilation: | no |
| Packaged: | 2022-08-22 10:37:03 UTC; Lenovo |
| Author: | Wei Ling [aut, cre], Yang Liu [aut] |
| Maintainer: | Wei Ling <lingwei3418@163.com> |
| Repository: | CRAN |
| Date/Publication: | 2022-08-22 12:50:08 UTC |
Distribution Recovery with the COS method for Different parameters
Description
Restore the distribution with the COS method under different parameters settings for error analysis.
Usage
CosPdfMulti(x, Chf, N, a, b)
Arguments
x |
vector of observations |
Chf |
the characteristic function |
N |
the number of cos term for summation |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
Value
A matrix that contains restored p.d.f. with different parameters
Examples
N <- 2**(1:6)
x <- seq(-5, 5, by = 10 / (32 - 1))
a <- -10.0
b <- 10.0
CosPdfMulti(x, StNormChf, N, a, b)
Distribution Recovery with the COS method
Description
Restore the distribution with the characteristic function through the COS method, an option pricing method based on the Fourier-cosine series.
Usage
CosPdfRecovery(x, Chf, N, a, b)
Arguments
x |
vector of observations |
Chf |
the characteristic function |
N |
the number of cos term for summation |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
Value
The approximated probability density of x
References
Fang F. and Oosterlee C.W. 2008. "A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions", Siam Journal on Scientific Computing. 31(2): 826-848. doi: 10.1137/080718061.
Examples
N <- 32
x <- seq(-5, 5, by = 10 / (32 - 1))
a <- -6.0
b <- 6.0
CosPdfRecovery(x, StNormChf, N, a, b)
Approximate the Option Price with the COS Method
Description
Approximate the standard European call option price with the COS method, an option pricing method based on the Fourier-cosine series.
Usage
CosValueOption(ValueOption, GBMChf, r, tau, N, a, b, method = "integrate")
Arguments
ValueOption |
the value function of the option |
GBMChf |
the characteristic function for GBM |
r |
the |
tau |
the |
N |
the number of cos term for summation |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
method |
how to calculate the integral, one of "integrate" and "jiahe" |
Value
The approximated euro call option price
References
Fang F. and Oosterlee C.W. 2008. "A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions", Siam Journal on Scientific Computing. 31(2): 826-848. doi: 10.1137/080718061.
Examples
r <- 0.1
sigmaS0 <- 0.2
tau <- 10
S0 <- 1
K <- 1
mu <- log(S0) + (r - 0.5 * sigmaS0^2) * tau
sigma <- sigmaS0 * sqrt(tau)
a <- -10
b <- 10
N <- 64
GBMChf <- function(u){NormChf(u,mu,sigma)}
ValueOption <- function(x){EuroCallOption(x,K)}
CosValueOption(ValueOption, GBMChf,r,tau, N, a, b)
Summary Statistics
Description
Calculate useful statistics for an multivariate data.
Usage
Describe(data, digits = 2)
Arguments
data |
vector of observations |
digits |
integer deciding the number of decimal places |
Value
A tibble of statistics, including min, max, mean, sd, Q25, Q50, Q75, kurt, Skew, n, na
Examples
swan <- rGarch(len = 180)
Describe(tibble(a1 = swan, a2 = swan + 1), 2)
Summary Statistics of Vector
Description
Calculate useful statistics for an univariate data.
Usage
DescribeVector(data, digits = 2)
Arguments
data |
vector of observations |
digits |
integer deciding the number of decimal places |
Value
A tibble of statistics, including min, max, mean, sd, Q25, Q50, Q75, kurt, Skew, n, na
Examples
swan <- rGarch(len = 180)
DescribeVector(swan)
The Value Function of European Call Option
Description
With global variable K, the strike price, calculate the value of European call option.
Usage
EuroCallOption(x, K)
Arguments
x |
the stock price |
K |
the strike price |
Value
The value of European call option
Examples
EuroCallOption(x = 2,K = 1)
F_k Coefficients
Description
Calculate the F_k coefficients for the COS method, an option pricing method based on the Fourier-cosine series.
Usage
F_k(Chf, N, a, b)
Arguments
Chf |
the characteristic function |
N |
the number of cos term for summation |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
Value
A vector of F_k coefficients
References
Fang F. and Oosterlee C.W. 2008. "A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions", Siam Journal on Scientific Computing. 31(2): 826-848. doi: 10.1137/080718061.
Examples
N <- 32
a <- -6.0
b <- 6.0
F_k(StNormChf, N, a, b)
Buy and Hold Backtest
Description
Backtest for the buy and hold with a fixed weights strategy.
Usage
FixBacktest(rets, weights)
Arguments
rets |
historic multivariate returns |
weights |
holding weights of stock |
Value
A backtest return series
Examples
names <- c("swan", "bear", "tiger")
date <- as.Date("2015-01-01") + days(0:179)
mu <- c(0.2, 0.08, 0.1)
sigma <- matrix(c(1, 0.25, -0.3, 0.25, 0.25, 0, -0.3, 0, 0.36), 3, 3)
allret <- rMvReturnSim(names, date, mu, sigma)
tsret <- as.timeSeries(allret)
FixBacktest(tsret, rep(1 / 3, 3))
Construct Portfolio
Description
Construct four types portfolio with specificition and constraints.
Usage
InvestmentPortfolio(data, method, spec, constraints = "LongOnly")
Arguments
data |
multivariate returns, must be "timeSeries" type |
method |
porofolio type, one of "fea", "minrisk", "globalminrisk" and "sharp" |
spec |
specificition of portfolio |
constraints |
constraints of trade |
Value
A portfolio
References
Markowitz H. 1952. "Portfolio Selection", The Journal of Finance, 7(1), 77–91. doi: 10.2307/2975974.
Examples
library(fPortfolio)
names <- c("swan", "bear", "tiger")
date <- as.Date("2015-01-01") + days(0:179)
mu <- c(0.2, 0.08, 0.1)
sigma <- matrix(c(1, 0.25, -0.3, 0.25, 0.25, 0, -0.3, 0, 0.36), 3, 3)
allret <- rMvReturnSim(names, date, mu, sigma)
tsret <- as.timeSeries(allret)
feaSpec <- portfolioSpec()
setWeights(feaSpec) <- rep(1 / 3, times = 3)
InvestmentPortfolio(tsret, "fea", feaSpec)
Calculate the Absolute Error of the COS Method
Description
Calculate the max absolute error of the cos method for different parameters given a vector of x.
Usage
LogErrorCosPdf(x, f, Chf, a, b, N)
Arguments
x |
vector of observations |
f |
the true p.d.f. |
Chf |
the characteristic function |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
N |
the number of cos term for summation |
Value
A matrix that contains the log max error for different parameters
Examples
N <- c(1:200)
L <- c(10, 20, 60, 100, 1000)
a <- -L / 2
b <- L / 2
x <- seq(-5, 5, by = 10 / (32 - 1))
LogErrorCosPdf(x, dnorm, NormChf, a, b, N)
The Characteristic Function of Normal Distribution
Description
The Characteristic Function of Normal Distribution
Usage
NormChf(u, mu = 0, sigma = 1)
Arguments
u |
observation |
mu |
the |
sigma |
the |
Value
The value of Characteristic Function
Examples
NormChf(1)
Plot the Probability Density Functions
Description
Plot the p.d.f functions for the univariate distribution with data processed by StackRet.
Usage
PdfMultiPlot(data, x, y, Variable)
Arguments
data |
a tibble contains x, y and Variable and the last one is the group variable |
x |
x |
y |
y |
Variable |
the group label |
Value
A ggplot figure of the probability density functions
Examples
N <- 2**(1:6)
x <- seq(-5, 5, by = 10 / (32 - 1))
a <- -10.0
b <- 10.0
f_x1 <- CosPdfMulti(x, StNormChf, N, a, b)
colnames(f_x1) <- paste("N = 2 ^ ", c(1:6), sep = "")
mt1 <- StackRet(f_x1, x)
colnames(mt1) <- c("x", "y", "Variable")
PdfMultiPlot(mt1, x, y, Variable)
Plot the Probability Density Function
Description
Plot the p.d.f function for the univariate distribution with x and y.
Usage
PdfSinglePlot(data, x, y)
Arguments
data |
a tiible contains x and y |
x |
x |
y |
y |
Value
A ggplot figure of the probability density function
Examples
N <- 32
x <- seq(-5, 5, by = 10 / (32 - 1))
a <- -6.0
b <- 6.0
f_x <- CosPdfRecovery(x, StNormChf, N, a, b)
tnorm <- tibble(x = x, y = f_x)
PdfSinglePlot(tnorm, x, y)
Calculate Useful Indicators for returns
Description
Calculate cumulative return, annualized return, max drawdown, annualized sharp ratio, calmar ratio, sortino ratio, alpha, beta and information ratio with returns.
Usage
RiskIndicators(ret, rb, rf = 0)
Arguments
ret |
vector of return |
rb |
return of market portfolio |
rf |
risk free rate |
Value
A matrix of return and risk indicators
Examples
date <- as.Date("2015-01-01") + days(0:249)
ret <- as.xts(rnorm(250), date)
rb <- as.xts(rep(0, 250), date)
RiskIndicators(ret, rb = rb, rf = 0)
Calculate Sharp Ratio with stock prices
Description
Calculate sharp ratio of stock with running window.
Usage
Sharp(x, rf = 0, n = 10)
Arguments
x |
vector of price |
rf |
risk free rate |
n |
the length of running window |
Value
The sharp ratio series with length the same as x
Examples
date <- as.Date("2015-01-01") + days(0:29)
trade <- rTrade(date)
x <- trade$Close
Sharp(x)
The Characteristic Function of Standard Normal Distribution
Description
The Characteristic Function of Standard Normal Distribution
Usage
StNormChf(u)
Arguments
u |
observation |
Value
The value of Characteristic Function
Examples
StNormChf(1)
Rearrange the data from LogErrorCosPdf for plot
Description
Rearrange the data from LogErrorCosPdf for plot
Usage
StackForPlot(error, a, b, N)
Arguments
error |
return of |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
N |
the number of cos term for summation |
Value
Suitable tibble data for plot by group in ggplot
Examples
N <- c(1:200)
L <- c(10, 20, 60, 100, 1000)
a <- -L / 2
b <- L / 2
x <- seq(-5, 5, by = 10 / (32 - 1))
el <- LogErrorCosPdf(x, dnorm, NormChf, a, b, N)
StackForPlot(el, a, b, N)
Stack Rets for ggplot
Description
Change the arrangement of multivariate data to generate suitable data for ggplot.
Usage
StackRet(rets, date)
Arguments
rets |
multivariate data, arranged by column |
date |
vector of common information for variables |
Value
Suitable tibble data for plot by group in ggplot
Examples
names <- c("swan", "bear", "tiger")
date <- as.Date("2015-01-01") + days(0:179)
mu <- c(0.2, 0.08, 0.1)
sigma <- matrix(c(1, 0.25, -0.3, 0.25, 0.25, 0, -0.3, 0, 0.36), 3, 3)
allret <- rMvReturnSim(names, date, mu, sigma)
StackRet(allret, date)
V_k Series
Description
Calculate the V_k Series for Option Pricing with the COS Method, an option pricing method based on the Fourier-cosine series.
Usage
V_k(ValueOption, N, a, b, method = "integrate")
Arguments
ValueOption |
the value function of the option |
N |
the number of cos term for summation |
a |
the lower limit of the truncation interval |
b |
the upper limit of the truncation interval |
method |
how to calculate the integral, one of "integrate" and "jiahe" |
Value
The V_k series
References
Fang F. and Oosterlee C.W. 2008. "A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions", Siam Journal on Scientific Computing. 31(2): 826-848. doi: 10.1137/080718061.
Examples
r <- 0.1
sigmaS0 <- 0.2
tau <- 10
S0 <- 1
K <- 1
mu <- log(S0) + (r - 0.5 * sigmaS0^2) * tau
sigma <- sigmaS0 * sqrt(tau)
a <- -10
b <- 10
N <- 64
ValueOption <- function(x){EuroCallOption(x,K)}
V_k(ValueOption, N, a, b)
VaR Calculation and Coverage Test
Description
Calculate VaR with three method and implement unconditional and conditional coverage test.
Usage
VaRSimTest(data, method, alpha, fun, ...)
Arguments
data |
vector of returns |
method |
the VaR method, one of "param", "hist" and "mc" |
alpha |
the VaR confidence level |
fun |
function calculating VaR, limited by |
... |
the extra parameters of |
Value
A list of VaR and coverage test outcome
References
Christoffersen P. F. 1998. "Evaluating Interval Forecasts", International Economic Review, 841-862. doi: 10.2307/2527341.
Kupiec PH. 1995. "Techniques for Verifying the Accuracy of Risk Measurement Models", The Journal of Derivatives, 3(2), 73-84. doi: 10.3905/jod.1995.407942.
Examples
swan <- rGarch(len = 30)
date <- as.Date("2015-01-01") + days(0:(length(swan) - 1))
tswan <- tibble(garch = swan, date = date)
tsswan <- as.xts(swan, date)
alpha = 0.05
num = 100000
mu = mean(tsswan)
sd = sd(tsswan)
VaRSimTest(tsswan, "mc", alpha , rnorm, 100000, mu, sd)
Plot the Acf Figure
Description
Plot the Acf figure with observations of a single variable beautifully.
Usage
ggacf(data, lag = 10)
Arguments
data |
vector of observations |
lag |
the maximum lag to calculate the acf |
Value
A ggplot figure of the acf
Examples
swan <- rGarch(len = 180)
ggacf(swan^2, 20)
Plot the Box Figure
Description
Plot the box figure beautifully with ggplot.
Usage
ggboxplot(data, mapping)
Arguments
data |
a tibble |
mapping |
the mapping parameter of ggplot |
Value
A box figure by ggplot
Examples
names <- c("swan", "bear", "tiger")
date <- as.Date("2015-01-01") + days(0:179)
mu <- c(0.2, 0.08, 0.1)
sigma <- matrix(c(1, 0.25, -0.3, 0.25, 0.25, 0, -0.3, 0, 0.36), 3, 3)
allret <- rMvReturnSim(names, date, mu, sigma)
totret <- StackRet(allret, date)
ggboxplot(totret, aes(x = stock, y = ret))
Plot the Histogram Figure
Description
Plot the histgram figure beautifully with ggplot.
Usage
gghistplot(data, mapping, bins = 10)
Arguments
data |
a tibble |
mapping |
the mapping parameter |
bins |
the number of bins |
Value
A histogram figure by ggplot
Examples
date <- as.Date("2015-01-01") + days(0:180)
thero <- returns(rGbm("thero", date))[-1]
tthero <- tibble(x = date[-1], y = thero)
gghistplot(tthero, aes(x = thero, y = stat(density)), bins = 20)
Plot the Time Series
Description
Plot the time series data beautifully with ggplot.
Usage
gglineplot(data, mapping, date_labels = "%Y/%m/%d", date_breaks = "2 weeks")
Arguments
data |
a tibble |
mapping |
the mapping parameter |
date_labels |
the x label |
date_breaks |
the period of the x label |
Value
A ggplot figure of the time series
Examples
date <- as.Date("2015-01-01") + days(0:180)
thero <- returns(rGbm("thero", date))[-1]
tthero <- tibble(x = date[-1], y = thero)
gglineplot(tthero, aes(x, y), "%Y/%m", "1 months")
Plot the Pacf Figure
Description
Plot the Pacf figure with observations of a single variable beautifully.
Usage
ggpacf(data, lag = 10)
Arguments
data |
vector of observations |
lag |
the maximum lag to calculate the pacf |
Value
A ggplot figure of the pacf
Examples
swan <- rGarch(len = 180)
ggpacf(swan^2, 20)
Simulate a Garch Series
Description
Simulate a Garch series given its data generate process with mean part.
Usage
rGarch(
u = 0,
a0 = rnorm(1, 0, 1),
sigma20 = rnorm(1, 0, 1)^2,
alpha = c(0.5, 0.5),
beta = 0.25,
len = 10
)
Arguments
u |
the mean series |
a0 |
vector of the start part |
sigma20 |
vector of the initial variance |
alpha |
the |
beta |
the |
len |
the length, include defined |
Value
A simulated garch series
References
Bollerslev T. 1986. "Generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 31(3): 307-327. doi: 10.1016/0304-4076(86)90063-1.
Examples
rGarch()
Simulate a Garch Series
Description
Simulate a Garch series given its data generate process without mean part.
Usage
rGarcha(
a0 = rnorm(1, 0, 1),
sigma20 = rnorm(1, 0, 1)^2,
alpha = c(0.5, 0.5),
beta = 0.25,
len = 10
)
Arguments
a0 |
vector of the start part |
sigma20 |
vector of the initial variance |
alpha |
the |
beta |
the |
len |
the length, include defined |
Value
A simulated garch series
References
Bollerslev T. 1986. "Generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 31(3): 307-327. doi: 10.1016/0304-4076(86)90063-1.
Examples
rGarcha()
Simulate prices series of stocks
Description
Simulate an multivariate series following Geometric Brownian Motion (GBM)
Usage
rGbm(name, time, start = 100, mu = 0.01, sigma = 0.02)
Arguments
name |
vector of series names |
time |
vector of time, must be a "Date" type variable |
start |
vector of start positions |
mu |
vector of |
sigma |
vector of |
Value
a simulated multivariate GBM series
Examples
date <- as.Date("2015-01-01") + days(0:29)
rGbm(c("bear", "tiger", "swan"), date)
Simulate a single stock price series
Description
Simulate an univariate series following Geometric Brownian Motion (GBM).
Usage
rGbmSingle(len, start = 100, mu = 0.01, sigma = 0.02)
Arguments
len |
the length |
start |
the start position |
mu |
the |
sigma |
the |
Value
a simulated univariate GBM series
Examples
rGbmSingle(100)
Simulate Multivariate Stocks Prices Data
Description
Simulate multivariate prices for interconnected stocks with each price series following Geometric Brownian Motion (GBM).
Usage
rGbms(
name,
len,
start = c(1000, 1000),
mu = rep(1e-04, 2),
sigma = matrix(c(2e-04, 1e-04, 1e-04, 2e-04), 2, 2),
digits = 2
)
Arguments
name |
vector of series names |
len |
the length |
start |
vector of start positions |
mu |
vector of |
sigma |
vector of |
digits |
integer deciding the number of decimal places |
Value
A simulated multivariate GBM series with each series interconnected
Examples
rGbms(c("bear", "tiger"), len = 36)
Simulate Stocks Prices
Description
Simulate stocks prices following multivariate normal distribution.
Usage
rMvReturnSim(
names,
date,
mu = rep(0, 2),
sigma = matrix(c(1, 0.5, 0.5, 1), 2, 2)
)
Arguments
names |
vector of names |
date |
vector of time, must be "Date" type |
mu |
vector of |
sigma |
vector of |
Value
Multivariate stock prices
Examples
names <- c("swan", "bear")
date <- as.Date("2015-01-01") + days(0:29)
rMvReturnSim(names, date)
Simulate stock trade data
Description
Simulate stock trade data with assumption that the stock price following Geometric Brownian Motion (GBM).
Usage
rTrade(time, start = 100, mu = 1e-04, sigma = 2e-04)
Arguments
time |
time vector of time, must be a "Date" type variable |
start |
the start position |
mu |
the |
sigma |
the |
Value
Stock trade data with Open, High, Low and Close
Examples
date <- as.Date("2015-01-01") + days(0:29)
rTrade(date)
Simulate Multivariate Stock Trade Data
Description
Simulate multivariate stock trade data with assumption that each stock price following Geometric Brownian Motion (GBM). And these prices are interconnected.
Usage
rTrades(
name,
time,
start = c(1000, 1000),
mu = rep(1e-04, 2),
sigma = matrix(c(2e-04, 1e-04, 1e-04, 2e-04), 2, 2),
digits = 2
)
Arguments
name |
vector of names |
time |
time vector of time, must be "Date" type |
start |
vector of start positions |
mu |
vector of |
sigma |
vector of |
digits |
integer deciding the number of deciamal places |
Value
A list of stock trade data with Open, High, Low and Close
Examples
date <- as.Date("2015-01-01") + days(0:29)
rTrades(c("swan", "bear"), date)