Package 'RcmdrPlugin.RiskDemo' reference manual

Title:	R Commander Plug-in for Risk Demonstration
Description:	R Commander plug-in to demonstrate various actuarial and financial risks. It includes valuation of bonds and stocks, portfolio optimization, classical ruin theory, demography and epidemic.
Authors:	Arto Luoma
Maintainer:	Arto Luoma <[email protected]>
License:	GPL-2
Version:	3.2
Built:	2024-11-03 04:52:29 UTC
Source:	https://github.com/cran/RcmdrPlugin.RiskDemo

R Commander Plug-in for Risk Demonstration

Description

R Commander plug-in to demonstrate various actuarial and financial risks. It includes valuation of bonds and stocks, portfolio optimization, classical ruin theory, demography and epidemic.

Details

Package:	RcmdrPlugin.RiskDemo
Type:	Package
Version:	3.0
Date:	2021-04-03
License:	GPL (>= 2)
LazyLoad:	yes

Author(s)

Arto Luoma

Maintainer: Arto Luoma <[email protected]>

Drawing forward and yield curves

Description

This function draws forward and yields curves, for AAA-rated central governement bonds and/or all central governement bonds.

Usage

bondCurve(date1, date2 = NULL, yield = TRUE, forward = TRUE, 
  AAA = TRUE, all = TRUE, params)
bondCurve(date1, date2 = NULL, yield = TRUE, forward = TRUE, 
  AAA = TRUE, all = TRUE, params)

Arguments

`date1`	The date for which the curves are drawn
`date2`	Optional second date for which the curves are drawn
`yield`	Is the yield curve shown (TRUE/FALSE)?
`forward`	Is the forward curve shown (TRUE/FALSE)?
`AAA`	Are the curves drawn for the AAA-rated bonds (TRUE/FALSE)?
`all`	Are the curves drawn for the bonds with all ratings (TRUE/FALSE)?
`params`	The data frame of curve parameters

Value

No value. Only a figure is produced.

Author(s)

Arto Luoma

References

https://bit.ly/2zfs0G8

Examples

data(params)
bondCurve(as.Date("2004-09-06"),params=params)
data(params)
bondCurve(as.Date("2004-09-06"),params=params)

Bond price as a function of interest rate.

Description

This function plots the bond price as a function of interest rate. It also shows, using dotted lines, the yield to maturity rate corresponding to the face value, and the flat price corresponding to the yield to maturity.

Usage

bondFigure(buyDate, matDate, rateCoupon, yieldToMat = NULL, 
           bondPr = NULL, nPay)
bondFigure(buyDate, matDate, rateCoupon, yieldToMat = NULL, 
           bondPr = NULL, nPay)

Arguments

`buyDate`	the date when the coupon is bought (settlement date)
`matDate`	maturity date
`rateCoupon`	coupon rate (in decimals)
`yieldToMat`	yield to maturity (in decimals)
`bondPr`	the flat price of the bond
`nPay`	number of coupon payments per year

Details

either yieldToMat or bondPr should be given as input.

Value

This function only plots a figure.

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 14.2 Bond Pricing).

Examples

bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,yieldToMat=0.0079,
           nPay=2)
bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,bondPr=90,nPay=2)
bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,yieldToMat=0.0079,
           nPay=2)
bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,bondPr=90,nPay=2)

Computing bond prices

Description

This function computes the bond price, given the yield to maturity.

Usage

bondPrice(buyDate, matDate, rateCoupon, yieldToMat, nPay)
bondPrice(buyDate, matDate, rateCoupon, yieldToMat, nPay)

Arguments

`buyDate`	the date at which the bond is bought (settlement date).
`matDate`	maturity date
`rateCoupon`	annual coupon date
`yieldToMat`	yield to maturity
`nPay`	number of coupon payments per day

Details

All the rates are given in decimals.

Value

A list with the following components:

`yieldToMaturity`	yield to maturity
`flatPrice`	flat price
`daysSinceLastCoupon`	days since previous coupon payment
`daysInCouponPeriod`	days in a coupon period
`accruedInterest`	accrued interest since last coupon payment
`invoicePrice`	invoice price (= flat price + accrued interest)

Note

With Excel functions PRICE, DATE, COUPDAYBS and COUPDAYS you can do the same.

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Bond Pricing between Coupon Dates in Section 14.2).

Examples

bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,2)
bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,4)
bondPrice("2012-7-31","2030-5-15",0.0625,0.02117,2)
bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,2)
bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,4)
bondPrice("2012-7-31","2030-5-15",0.0625,0.02117,2)

Ruin probability computation with infinite time horizon

Description

This function uses classical ruin theory to compute either ruin probability, safety loading or initial capital, given two of them. The time horizon is infinite. Gamma distribution is used to model claim sizes.

Usage

computeRuin(U0 = NULL, theta = NULL, eps = NULL, alpha, beta)
computeRuin(U0 = NULL, theta = NULL, eps = NULL, alpha, beta)

Arguments

`U0`	initial capital
`theta`	safety loading
`eps`	ruin probability
`alpha`	shape parameter of gamma distribution
`beta`	rate parameter of gamma distribution

Value

The value is a list with the following components:

`LundbergExp`	Lundberg's exponent R
`initialCapital`	initial capital
`safetyLoading`	safety loading
`ruinProb`	ruin probability

Author(s)

Arto Luoma <[email protected]>

References

Gray and Pitts (2012) Risk Modelling in General Insurance: From Principles to Practice, Cambridge University Press.

Examples

computeRuin(U0=1000,theta=0.01,alpha=1,beta=0.1)
computeRuin(eps=0.005,theta=0.01,alpha=1,beta=0.1)
computeRuin(U0=5399.24,eps=0.005,alpha=1,beta=0.1)
computeRuin(U0=1000,theta=0.01,alpha=1,beta=0.1)
computeRuin(eps=0.005,theta=0.01,alpha=1,beta=0.1)
computeRuin(U0=5399.24,eps=0.005,alpha=1,beta=0.1)

Ruin probability computation with finite time horizon

Description

This function uses classical ruin theory to compute either ruin probability, safety loading or initial capital, given two of them. The time horizon is finite. Gamma distribution is used to model claim sizes.

Usage

computeRuinFinite(T0, U0 = NULL, theta = NULL, eps = NULL, lambda, 
                  alpha, beta)
computeRuinFinite(T0, U0 = NULL, theta = NULL, eps = NULL, lambda, 
                  alpha, beta)

Arguments

`T0`	time horizon (in years)
`U0`	initial capital
`theta`	safety loading
`eps`	ruin probability
`lambda`	claim intensity (mean number of claims per year)
`alpha`	shape parameter of gamma distribution
`beta`	rate parameter of gamma distribution

Value

The value is a list with the following components:

`LundbergExp`	Lundberg's exponent R
`initialCapital`	initial capital
`safetyLoading`	safety loading
`ruinProb`	ruin probability

Author(s)

Arto Luoma <[email protected]>

Examples

computeRuinFinite(T0=100,U0=1000,theta=0.01,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=1,eps=0.005,theta=0.001,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=500,U0=5347,eps=0.005,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=100,U0=1000,theta=0.01,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=1,eps=0.005,theta=0.001,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=500,U0=5347,eps=0.005,lambda=100,alpha=1,beta=0.1)

Mortality data

Description

Mortality data for 10 countries (period death rates and exposures) retrieved from Human Mortality Database. The data are rounded to three significant digits and include the Nordic countries, China, U.S., Russia, Japan and Germany.

Usage

data("countries.mort")data("countries.mort")

Format

List of objects of class demogdata.

Source

HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at www.mortality.org. (Data downloaded Nov 13, 2023.)

Examples

data(countries.mort)
plot(countries.mort[[1]])
data(countries.mort)
plot(countries.mort[[1]])

Kalman smoothing of the covid model

Description

This function does Kalman smoothing for the simple model that is used to predict new COVID-19 cases.

Usage

covidSmooth(par, y)
covidSmooth(par, y)

Arguments

`par`	Logarithms of the variance parameters of drift, seasonal component, and error term
`y`	Univariate numeric time series of new COVID-19 cases

Details

See loglikCovid.

Value

`Xif`	Matrix of filtered values, where the state vectors are given as rows
`Xis`	Matrix of smoothed values, where the state vectors are given as rows
`Pmat`	Array of state uncertainty matrices, evaluated at time t-1. The first array index is for time.
`Pfmat`	Array of state uncertainty matrices, evaluated at time t. The first array index is for time.
`Psmat`	Array of state uncertainty matrices, evaluated at time n, where n is the number of observations. The first array index is for time.

Author(s)

Arto Luoma

Examples

#Preparing a time series
library(zoo)
data(dataCovidFin)
timeindex <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","Aika"]
series <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","val"]
series <- window(zoo(series,order.by=timeindex),start="2020-03-01",
                 end="2021-03-01") 
#Fitting a state space model and smoothing the components
p0 <- c(-9,-7,-3.3)
fit <- nlm(loglikCovid,p=p0,y=series)
out <- covidSmooth(fit$estimate,y=series)

#Plotting the filtered and smoothed components
smoothed <- zoo(out$Xis[,1:3],order.by=time(series))
filtered <- zoo(out$Xif[,1:3],order.by=time(series))
colnames(smoothed) <- colnames(filtered) <- c("Level","Drift","Seasonal")
plot(filtered,xlab="Time",main="Filtered components of the time series")
plot(smoothed,xlab="Time",main="Smoothed components of the time series")

#Plotting the original time series, and the filtered and smoothed local level 
#series after transforming them to original scale
plot(series,xlab="Time",ylab="Time series")
lines(exp(filtered[,1])-2,col=3)
lines(exp(smoothed[,1])-2,col=2)
legend("topleft",c("original","filtered","smoothed"),col=c(1,3,2),lty=1)
#Preparing a time series
library(zoo)
data(dataCovidFin)
timeindex <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","Aika"]
series <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","val"]
series <- window(zoo(series,order.by=timeindex),start="2020-03-01",
                 end="2021-03-01") 
#Fitting a state space model and smoothing the components
p0 <- c(-9,-7,-3.3)
fit <- nlm(loglikCovid,p=p0,y=series)
out <- covidSmooth(fit$estimate,y=series)

#Plotting the filtered and smoothed components
smoothed <- zoo(out$Xis[,1:3],order.by=time(series))
filtered <- zoo(out$Xif[,1:3],order.by=time(series))
colnames(smoothed) <- colnames(filtered) <- c("Level","Drift","Seasonal")
plot(filtered,xlab="Time",main="Filtered components of the time series")
plot(smoothed,xlab="Time",main="Smoothed components of the time series")

#Plotting the original time series, and the filtered and smoothed local level 
#series after transforming them to original scale
plot(series,xlab="Time",ylab="Time series")
lines(exp(filtered[,1])-2,col=3)
lines(exp(smoothed[,1])-2,col=2)
legend("topleft",c("original","filtered","smoothed"),col=c(1,3,2),lty=1)

COVID-19 statistics

Description

This data set consists of several statistics about the COVID-19 pandemic in 45 countries.

Usage

data("dataCovid")data("dataCovid")

Format

A data frame with 18400 observations on the following 27 variables.

location: a character vector
date: a Date
new_cases: a numeric vector
new_cases_per_million: a numeric vector
new_cases_smoothed_per_million: a numeric vector
new_cases_smoothed: a numeric vector
new_deaths_per_million: a numeric vector
new_deaths: a numeric vector
new_deaths_smoothed_per_million: a numeric vector
new_deaths_smoothed: a numeric vector
total_deaths_per_million: a numeric vector
total_deaths: a numeric vector
total_cases: a numeric vector
total_cases_per_million: a numeric vector
hosp_patients: a numeric vector
hosp_patients_per_million: a numeric vector
icu_patients_per_million: a numeric vector
icu_patients: a numeric vector
reproduction_rate: a numeric vector
new_tests: a numeric vector
new_tests_per_thousand: a numeric vector
tests_per_case: a numeric vector
positive_rate: a numeric vector
new_tests_smoothed: a numeric vector
new_tests_smoothed_per_thousand: a numeric vector
total_tests: a numeric vector
total_tests_per_thousand: a numeric vector

Details

This is a subset of the complete data set available online, downloaded on March 31, 2021.

Source

https://covid.ourworldindata.org/data/owid-covid-data.csv

Examples

library(zoo)
data(dataCovid)
casesFin <- subset(dataCovid,subset=location=="Finland", select=c(date,new_cases))
plot(zoo(casesFin$new_cases,order.by=casesFin$date),ylab="New COVID-19 cases in Finland",
xlab="")
library(zoo)
data(dataCovid)
casesFin <- subset(dataCovid,subset=location=="Finland", select=c(date,new_cases))
plot(zoo(casesFin$new_cases,order.by=casesFin$date),ylab="New COVID-19 cases in Finland",
xlab="")

Confirmed COVID-19 cases in Finland

Description

This data set provides the confirmed COVID-19 cases in 21 Finnish hospital districts, in addition to the total number.

Usage

data("dataCovidFin")data("dataCovidFin")

Format

A data frame with 16082 observations on the following 3 variables.

Aika: Date
Alue: character vector: hospital district
val: numeric vector: number of new confirmed cases

Details

The data were downloaded on March 31, 2021, via THL's open data API.

Source

https://bit.ly/2PO1DnS

References

https://bit.ly/3ryfwE4

Examples

library(zoo)
data(dataCovidFin)
casesFin <- subset(dataCovidFin, subset = Alue=="Kaikki Alueet")
plot(zoo(casesFin$val,order.by=casesFin$Aika),ylab="New COVID-19 cases in Finland",xlab="")
library(zoo)
data(dataCovidFin)
casesFin <- subset(dataCovidFin, subset = Alue=="Kaikki Alueet")
plot(zoo(casesFin$val,order.by=casesFin$Aika),ylab="New COVID-19 cases in Finland",xlab="")

Plotting epidemic statistics

Description

This function plots several epidemic statistics for selected countries.

Usage

drawBars(data, countries, start = "2020-06-01", end = "last", measure = "new_cases", 
    atop = TRUE, perMillion = FALSE, drawMean = TRUE, bars = TRUE)
drawBars(data, countries, start = "2020-06-01", end = "last", measure = "new_cases", 
    atop = TRUE, perMillion = FALSE, drawMean = TRUE, bars = TRUE)

Arguments

`data`	data frame similar to (or including the same columns as) `dataCovid`
`countries`	vector of characters srings indicating the countries for which the selected statistic is plotted
`start`	beginning date of the time window for which the statistic is plotted
`end`	ending date of the time window for which the statistic is plotted
`measure`	statistic to be plotted
`atop`	logical indicating if the bars of different countries are plotted on top of one another
`perMillion`	logical indicating if the statistic is proportioned to a population of million
`drawMean`	logical indicating if a smoothed curve is drawn
`bars`	logical indicating if bars are plotted

Value

No value.

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovid)
drawBars(data=dataCovid, countries=c('Finland','France'),start='2020-6-1',
         measure='new_cases',perMillion=TRUE)
data(dataCovid)
drawBars(data=dataCovid, countries=c('Finland','France'),start='2020-6-1',
         measure='new_cases',perMillion=TRUE)

Plotting epidemic statistics with Finnish data

Description

This function plots the new cases or total cases of an epidemic for selected regions in Finland.

Usage

drawBarsFin(data, pop, regions, start = "2020-06-01", end = "last", 
    measure = "new_cases", atop = TRUE, perMillion = FALSE, drawMean = TRUE, 
    bars = TRUE)
drawBarsFin(data, pop, regions, start = "2020-06-01", end = "last", 
    measure = "new_cases", atop = TRUE, perMillion = FALSE, drawMean = TRUE, 
    bars = TRUE)

Arguments

`data`	data frame including columns `Aika` (character string indicating the date), `Alue` (character string indicating the region) and `val` (numeric indicating the number of new cases)
`pop`	data frame including columns `Alue` (character string indicating the region) and `val` (integer indicating the population)
`regions`	vector of characters strings indicating the regions for which the selected statistic is plotted
`start`	beginning date of the time window for which the curve is plotted
`end`	ending date of the time window for which the curve is plotted
`measure`	statistic to be plotted
`atop`	logical indicating if the bars of different regions are plotted on top of one another
`perMillion`	logical indicating if the statistic is proportioned to a population of million
`drawMean`	logical indicating if a smoothed curve (rolling mean of 7 observations) is plotted
`bars`	logical indicating if bars are plotted

Value

No value.

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovidFin)
data(popRegionsFin)
drawBarsFin(dataCovidFin,popRegionsFin,regions=popRegionsFin$Alue[1:7])
data(dataCovidFin)
data(popRegionsFin)
drawBarsFin(dataCovidFin,popRegionsFin,regions=popRegionsFin$Alue[1:7])

Efficient frontier and return distribution figures

Description

Plots the efficient frontiers of risky investments and all investments. The optimum points corresponding to the risk aversion coefficient are indicated by dots. Further, the function plots a predictive return distribution figure.

Usage

drawFigure(symbol, yield, vol, beta, r = 1, 
  total = 1, indexVol = 20, nStocks = 7, balanceInt = 12, A = 10, 
  riskfree = FALSE, bor = FALSE)
drawFigure(symbol, yield, vol, beta, r = 1, 
  total = 1, indexVol = 20, nStocks = 7, balanceInt = 12, A = 10, 
  riskfree = FALSE, bor = FALSE)

Arguments

`symbol`	character vector of the symbols of the risky investments
`yield`	vector of yields (%)
`vol`	vector of volatilities (%)
`beta`	vector of betas (%)
`r`	risk-free interest rate (%)
`total`	total investment (for example in euros)
`indexVol`	volatility of market portfolio (%)
`nStocks`	number of risky investments in the portfolio
`balanceInt`	balancing interval of the portfolio in months
`A`	risk aversion coefficient (see details)
`riskfree`	is risk-free investment included in the portfolio (logical)
`bor`	is borrowing (negative risk-free investment) allowed (logical)

Details

The function uses the single-index model and Markovitz portfolio optimization model to find the optimum risky portfolio. The returns are assumed to be log-normally distributed. The maximized function is mu - 0.5*A*var where mu is expected return, A is risk aversion coefficient, and var is return variance.

Value

`portfolio`	allocation of the total investment (in euros)
`returnExpectation`	expected portfolio return
`returnDeviation`	standard deviation of the portfolio

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 7.4 The Markowitz Portfolio Optimization Model and Section 8.2 The Single-Index Model).

Examples

data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,drawFigure(symbol=rownames(stockData),yield=divYield,
  vol=vol,beta=beta,r=1,total=100,indexVol=10, 
  nStocks=5,balanceInt=12,A=10,riskfree=TRUE,bor=FALSE))
data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,drawFigure(symbol=rownames(stockData),yield=divYield,
  vol=vol,beta=beta,r=1,total=100,indexVol=10, 
  nStocks=5,balanceInt=12,A=10,riskfree=TRUE,bor=FALSE))

Plotting incidence curves of an epidemic

Description

This function plots incidence curves of an epidemic for selected countries. The incidences are new cases per 100 000 inhabitants within one or two weeks.

Usage

drawIncidence(data, countries, start = "2020-06-01", end = "last", weeks = 2, 
    log = TRUE)
drawIncidence(data, countries, start = "2020-06-01", end = "last", weeks = 2, 
    log = TRUE)

Arguments

`data`	data frame including columns `location` (character string indicating the country), `date` (character string) and `new_cases_per_million` (numeric)
`countries`	vector of characters srings indicating the countries for which the curves are plotted
`start`	beginning date of the time window for which the curve is plotted
`end`	ending date of the time window for which the curve is plotted
`weeks`	Integer telling how many weeks' observations are used to calculate the incidence. Usually 1 or 2.
`log`	logical indicating if a log scale is used in the plot

Value

No value

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovid)
Europe <- c("Germany","France","United Kingdom","Italy","Spain","Poland","Romania",
    "Netherlands","Belgium","Greece")
drawIncidence(dataCovid,countries=Europe)
data(dataCovid)
Europe <- c("Germany","France","United Kingdom","Italy","Spain","Poland","Romania",
    "Netherlands","Belgium","Greece")
drawIncidence(dataCovid,countries=Europe)

Plotting incidence curves of an epidemic with Finnish data

Description

This function plots incidence curves of an epidemic for selected regions of Finland. The incidences are new cases per 100 000 inhabitants within one or two weeks.

Usage

drawIncidenceFin(data, pop, regions, start = "2020-06-01", end = "last", weeks = 2, 
    includeAllRegions = TRUE, log = TRUE)
drawIncidenceFin(data, pop, regions, start = "2020-06-01", end = "last", weeks = 2, 
    includeAllRegions = TRUE, log = TRUE)

Arguments

`data`	data frame including columns `Aika` (character string indicating the date), `Alue` (character string indicating the region) and `val` (numeric indicating the number of new cases)
`pop`	data frame including columns `Alue` (character string indicating the region) and `val` (integer indicating the population)
`regions`	vector of characters srings indicating the regions for which the curves are plotted
`start`	beginning date of the time window for which the curve is plotted
`end`	ending date of the time window for which the curve is plotted
`weeks`	Integer telling how many weeks' observations are used to calculate the incidence. Usually 1 or 2.
`includeAllRegions`	logical indicating if a curve for total incidence is included
`log`	logical indicating if a log scale is used in the plot

Value

No value

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovidFin)
data(popRegionsFin)
drawIncidenceFin(data = dataCovidFin, pop = popRegionsFin, 
    regions = popRegionsFin$Alue[1:5], start = "2020-06-01", end="last", weeks=2, 
    includeAllRegions = TRUE)
data(dataCovidFin)
data(popRegionsFin)
drawIncidenceFin(data = dataCovidFin, pop = popRegionsFin, 
    regions = popRegionsFin$Alue[1:5], start = "2020-06-01", end="last", weeks=2, 
    includeAllRegions = TRUE)

Plotting the positive rate of COVID-19 tests or the tests per case

Description

This function plots a time series of either the positive rate of COVID-19 tests or the number of tests per case.

Usage

drawPositiveRate(data, countries, start = "2020-06-01", end = "last", 
    measure = "positive_rate", curve = TRUE, bars = FALSE, log = FALSE)
drawPositiveRate(data, countries, start = "2020-06-01", end = "last", 
    measure = "positive_rate", curve = TRUE, bars = FALSE, log = FALSE)

Arguments

`data`	data frame including columns `location` (character string indicating the country), `date` (character string) and `tests_per_case, positive_rate` (numeric)
`countries`	vector of characters srings indicating the countries for which the selected statistic is plotted
`start`	beginning date of the time window for which the time series are plotted
`end`	ending date of the time window for which the time series are plotted
`measure`	statistic for which the time series are plotted
`curve`	logical indicating if smoothed curves are drawn
`bars`	logical indicating if bars are plotted
`log`	logical indicating if a log scale is used in the plot

Value

No value.

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovid)
drawPositiveRate(dataCovid,countries=c("Finland","France"))
data(dataCovid)
drawPositiveRate(dataCovid,countries=c("Finland","France"))

Plotting simulations of a surplus process

Description

This function plots simulation paths of a surpluss process. The claims are assumed to arrive according to a Poisson process and the claim sizes are assumed to be gamma distributed.

Usage

drawRuin(nsim = 10, Tup = 10, U0 = 1000, theta = 0.01, 
         lambda = 100, alpha = 1, beta = 0.1)
drawRuin(nsim = 10, Tup = 10, U0 = 1000, theta = 0.01, 
         lambda = 100, alpha = 1, beta = 0.1)

Arguments

`nsim`	number of simulations
`Tup`	maximum value in the time axis
`U0`	initial capital
`theta`	risk loading
`lambda`	intensity of claim process (mean number of claims per year)
`alpha`	shape parameter of gamma distribution
`beta`	rate parameter of gamma distribution

Value

No value; only a figure is plotted.

Author(s)

Arto Luoma <[email protected]>

References

Kaas, Goovaerts, Dhaene, Denuit (2008) Modern actuarial risk theory using R, 2nd ed., Springer.

Examples

computeRuinFinite(T0=10,U0=1000,eps=0.05,lambda=100,alpha=1,beta=0.1)
drawRuin(nsim=10,Tup=10,U0=1000,theta=0.0125,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=10,U0=1000,eps=0.05,lambda=100,alpha=1,beta=0.1)
drawRuin(nsim=10,Tup=10,U0=1000,theta=0.0125,lambda=100,alpha=1,beta=0.1)

Plotting time series related to COVID-19 testing

Description

This function plots time series of new and total COVID-19 tests, possibly in proportion to population.

Usage

drawTests(data, countries, start = "2020-06-01", end = "last", measure = "new_tests", 
    atop = TRUE, perThousand = FALSE, drawMean = TRUE, bars = TRUE, log = FALSE)
drawTests(data, countries, start = "2020-06-01", end = "last", measure = "new_tests", 
    atop = TRUE, perThousand = FALSE, drawMean = TRUE, bars = TRUE, log = FALSE)

Arguments

`data`	data frame similar to (or including the same columns as) `dataCovid`
`countries`	vector of characters strings indicating the countries for which the time series are plotted
`start`	beginning date of the time window for which the time series are plotted
`end`	ending date of the time window for which the time series are plotted
`measure`	statistic for which the time series are plotted
`atop`	logical indicating if the bars of different countries are plotted on top of one another
`perThousand`	logical indicating if the statistic is proportioned to a population of thousand
`drawMean`	logical indicating if a smoothed curve is drawn
`bars`	logical indicating if bars are plotted
`log`	logical indicating if a log scale is used in the plot

Value

No value.

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovid)
drawTests(dataCovid,countries=c("Finland","France"),perThousand=TRUE)
data(dataCovid)
drawTests(dataCovid,countries=c("Finland","France"),perThousand=TRUE)

Mortality data for Finland

Description

Mortality data for Finland Series: female male total Years: 1878 - 2015 Ages: 0 - 110

Usage

data("fin")data("fin")

Format

object of class demogdata

Details

This is part of the countries.mort data (countries.mort[[11]]).

Source

Examples

data(fin)
print(fin)
plot(fin)
data(fin)
print(fin)
plot(fin)

Finnish mortality forecast

Description

Finnish mortality forecast 50 years ahead (2023-2072) for 0 - 100 years old. The forecast is based on an estimated Lee-Carter model. The kt coefficients were forecast using a random walk with drift. Fitted rates were used as the starting value.

Usage

data("fin.fcast")data("fin.fcast")

Format

An object of class "fmforecast"; for details, see documentation of package "demography".

Details

The forecast was produced using function "forecast.lca" of package "demography".

Examples

data(fin.fcast)
print(fin.fcast)
plot(fin.fcast)
data(fin.fcast)
print(fin.fcast)
plot(fin.fcast)

Lee-Carter model fit for Finnish data

Description

Lee-Carter model fit obtained by function "lca" of package "demography". The fit is based on Finnish mortality data for ages from 0 to 100 and years from 1950 to 2022.

Usage

data("fin.lca")data("fin.lca")

Format

object of class "lca"

Details

Both sexes were included in the input mortality data.

Examples

data(fin.lca)
plot(fin.lca) 
data(fin.lca)
plot(fin.lca)

Computing the log-likelihood of the covid model

Description

This function computes -2 times the log-likelihood of the simple model that is used to predict new COVID-19 cases and to estimate the effective reproduction number.

Usage

loglikCovid(y, par, it = TRUE)
loglikCovid(y, par, it = TRUE)

Arguments

`y`	Univariate numeric time series of new COVID-19 cases
`par`	Logarithms of the variance parameters of drift, seasonal component, and error term
`it`	A logical value indicating if only the log-likelihood is returned.

Details

Some multiplicative and additive constants are omitted when the negative log-likelihood is computed. Before computing the log-likelihood, the transformation y=log(x+a), where a=2, is applied to the time series. The model is a simple local linear model with local level, drift and seasonal component. The variance parameters of the level and seasonal component are estimated while the variance of the level component is computed as max(exp(xi[1]) - a, 0.1)/exp(xi[1])^2, where xi[1] is the current estimate of the level. This is based on the assumption that the number of new cases is approximately Poisson distributed, so that the variance equals the level. The max operation is taken in order to prevent the exression from being negative. In order to facilitate estimation, a penalty term is added which corresponds to a prior of N(-9,1) for the logarithm of the drift variance.

Value

`loglik`	-2 times the penalized log likelihood apart from some additive constants
`ll`	Vector of the increments of the log-likelihood corresponding to individual observations
`Xi`	Matrix of one-step predictions of the state vector. The vectors at different time points are given as rows.
`Xif`	Matrix of filtered values, where the state vectors are given as rows
`Pfmat`	Array of state uncertainty matrices, evaluated at time t. The first array index is for time.
`Q`	Covariance matrix of the error vector of the state equation

Author(s)

Arto Luoma <[email protected]>

References

Hamilton (1994) Time Series Analysis, Princeton University Press, (see Chapter 13 The Kalman Filter).

Examples

#See examples for covidSmooth.
#See examples for covidSmooth.

Yield curve parameter data

Description

Yield curve parameters from the European Central Bank (ECB), downloaded on Nov 4, 2023

Usage

data("params")data("params")

Format

A data frame with 4902 observations on the following 13 variables.

date: a Date
b0: a numeric vector
b1: a numeric vector
b2: a numeric vector
b3: a numeric vector
t1: a numeric vector
t2: a numeric vector
c0: a numeric vector
c1: a numeric vector
c2: a numeric vector
c3: a numeric vector
d1: a numeric vector
d2: a numeric vector

Details

The parameters b0 to b3 are the beta-parameters, and t1 and t2 the tau-parameters for AAA-rated government bonds. The parameters c0 to c3 are the beta-parameters, and d1 and d2 the tau-parameters for all government bonds.

Source

https://bit.ly/2zfs0G8

Examples

data(params)
bondCurve(as.Date("2004-09-06"),params=params)
data(params)
bondCurve(as.Date("2004-09-06"),params=params)

Forecasting new covid cases

Description

This function forecasts the numbers of new covid cases using a simple linear state space model.

Usage

plotForecast(data, region, start = NULL, end = NULL, np = 30, predInt = 0.95, 
    log = TRUE)
plotForecast(data, region, start = NULL, end = NULL, np = 30, predInt = 0.95, 
    log = TRUE)

Arguments

`data`	data frame including columns `Aika` (character string indicating the date), `Alue` (character string indicating the region) and `val` (numeric indicating the number of new cases)
`region`	characters string indicating the region for which the forecast is made
`start`	beginning date of the observations used in the estimation of the forecasting model
`end`	ending date of the observations used in the estimation of the forecasting model
`np`	integer indicating the forecasting horizon in days
`predInt`	decimal indicating the probability of the forecasting interval
`log`	logical indicating if a log scale is used in the plot

Value

No value.

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovidFin)
plotForecast(data=dataCovidFin, region='All regions', start="2020-09-01")
data(dataCovidFin)
plotForecast(data=dataCovidFin, region='All regions', start="2020-09-01")

Plotting the effective reproduction number (R)

Description

This function plots a time series of the effective reproduction number R and its confidence interval.

Usage

plotR(data, region, start = NULL, end = NULL, confInt = 0.95)
plotR(data, region, start = NULL, end = NULL, confInt = 0.95)

Arguments

`data`	data frame including columns `Aika` (character string indicating the date), `Alue` (character string indicating the region) and `val` (numeric indicating the number of new cases)
`region`	characters string indicating the region for which the R series is computed
`start`	beginning date of the time window for which the R is computed
`end`	ending date of the time window for which the R is computed
`confInt`	decimal between 0 and 1, indicating the level of the confidence interval of R

Value

No value

Author(s)

Arto Luoma <[email protected]>

Examples

data(dataCovidFin)
plotR(data=dataCovidFin, region='All regions')
data(dataCovidFin)
plotR(data=dataCovidFin, region='All regions')

Population forecasting

Description

Population forecasting using mortality forecast and simple time series forecast for age 0 population

Usage

pop.pred(mort, mort.fcast)
pop.pred(mort, mort.fcast)

Arguments

`mort`	mortality data of class 'demogdata'
`mort.fcast`	mortality forecast of class 'fmforecast'

Details

ARIMA(0,2,2)-model is used to forecast age 0 populaton.

Value

population forecast of class 'demogdata'

Author(s)

Arto Luoma <[email protected]>

Examples

data(fin)
data(fin.fcast)
fin.pcast <- pop.pred(fin,fin.fcast)
plot(fin,plot.type="functions",series="total",transform=FALSE,
     datatype="pop",ages=c(0:100), years=c(1990+0:5*10), xlab="Age")
lines(fin.pcast,plot.type="functions",series="total",transform=FALSE, 
      datatype="pop",ages=c(0:100), years=c(1990+0:5*10), lty=2)
data(fin)
data(fin.fcast)
fin.pcast <- pop.pred(fin,fin.fcast)
plot(fin,plot.type="functions",series="total",transform=FALSE,
     datatype="pop",ages=c(0:100), years=c(1990+0:5*10), xlab="Age")
lines(fin.pcast,plot.type="functions",series="total",transform=FALSE, 
      datatype="pop",ages=c(0:100), years=c(1990+0:5*10), lty=2)

Population data on Finnish hospital districts

Description

This data set provides the populations of the 21 hospital districts, in addition to the total Finnish population.

Usage

data("popRegionsFin")data("popRegionsFin")

Format

A data frame with 22 observations on the following 2 variables.

Alue: character vector: hospital district
val: numeric vector: population

Details

The data were downloaded on March 31, 2021, via THL's open data API.

Source

https://bit.ly/39uZy7C

References

https://bit.ly/3ryfwE4

Examples

data(popRegionsFin)
print(popRegionsFin)
data(popRegionsFin)
print(popRegionsFin)

Portfolio optimization for an index model

Description

Finds an optimal portfolio for long-term investments and plots a return distribution.

Usage

portfOptim(i, symbol, yield, vol, beta, 
  indexVol = 0.2, nStocks = 7, total = 1, balanceInt = 1, 
  C = 0.05, riskProportion = 1, riskfreeRate = 0, sim = FALSE)
portfOptim(i, symbol, yield, vol, beta, 
  indexVol = 0.2, nStocks = 7, total = 1, balanceInt = 1, 
  C = 0.05, riskProportion = 1, riskfreeRate = 0, sim = FALSE)

Arguments

`i`	vector of the indices of the included risky investments
`symbol`	character vector of the symbols of the risky investments
`yield`	vector of expected yields (in euros)
`vol`	vector of volatilities
`beta`	vector of betas
`indexVol`	portfolio index volatility
`nStocks`	number of stocks in the portfolio
`total`	total sum invested (in euros)
`balanceInt`	balancing interval of the portfolio (in years)
`C`	expected portfolio return (in euros)
`riskProportion`	proportion of risky investments
`riskfreeRate`	risk-free interest rate
`sim`	is the return distribution simulated and plotted (logical value)?

Details

The arguments vol, beta, indexVol, riskProportion and riskfreeRate are given in decimals. The portfolio is optimized by minimizing the variance of the portfolio yield for a given expected yield. The returns are assumed to be log-normally distributed. The covariance matrix is computed using the single index model and the properties of the log-normal distribution.

Value

`portfolio`	numeric vector of allocations to each stock (in euros)
`returnExpectation`	expected value of the return distribution (in euros)
`returnDeviation`	standard deviation of the return distribution (in euros)
`VaR`	0.5%,1%,5%,10% and 50% percentiles of the return distribution (in euros)

Note

This function is usually called by drawFigure.

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 7.4 The Markowitz Portfolio Optimization Model and Section 8.2 The Single-Index Model).

Examples

data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,portfOptim(i=1:5,symbol=rownames(stockData),
  yield=divYield/100,vol=vol/100,beta=beta/100,total=100, sim=TRUE))
data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,portfOptim(i=1:5,symbol=rownames(stockData),
  yield=divYield/100,vol=vol/100,beta=beta/100,total=100, sim=TRUE))

Computing expected returns and their covariance matrix

Description

Computing expected returns and their covariance matrix when the returns are lognormal.

Usage

returns(volvec, indexvol, beta)
returns(volvec, indexvol, beta)

Arguments

`volvec`	vector of volatilities
`indexvol`	volatility of the portfolio index
`beta`	vector of betas

Details

The arguments are given in decimals. The single index model is used to compute the covariance matrix of a multivariate normal distribution. The mean vector is assumed to be zero. The properties of the log-normal distribution are then used to compute the mean vector and covariance matrix of the corresponding multivariate log-normal distribution.

Value

`mean`	vector of expected returns
`cov`	covariance matrix of returns

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 8.2 The Single-Index Model).

Examples

returns(volvec=c(0.1,0.2,0.3),indexvol=0.2, beta=c(0.5,-0.1,1.1)) 
returns(volvec=c(0.1,0.2,0.3),indexvol=0.2, beta=c(0.5,-0.1,1.1))

Solving Lund's exponent

Description

This function solves Lund's exponent or adjustment coefficient. The claim sizes are assumed to be gamma distributed.

Usage

solveLund(alpha, beta, theta)
solveLund(alpha, beta, theta)

Arguments

`alpha`	shape parameter of gamma distribution
`beta`	rate parameter of gamma distribution
`theta`	safety loading

Value

Lundberg's exponent (or adjustment coefficient)

Author(s)

Arto Luoma <[email protected]>

References

Gray and Pitts (2012) Risk Modelling in General Insurance: From Principles to Practice, Cambridge University Press.

Examples

solveLund(1,1,0.1)
solveLund(1,1,0.1)

Computing bond yields

Description

This function computes the yield to maturity, given the (flat) bond price.

Usage

solveYield(buyDate, matDate, rateCoupon, bondPr, nPay)
solveYield(buyDate, matDate, rateCoupon, bondPr, nPay)

Arguments

`buyDate`	settlement date (the date when the bond is bought)
`matDate`	maturity date
`rateCoupon`	annual coupon rate
`bondPr`	bond price. The flat price without accrued interest.
`nPay`	number of payments per year

Details

all the rates are given in decimals

Value

A list with the following components:

`yieldToMaturity`	yield to maturity
`flatPrice`	flat price
`daysSinceLastCoupon`	days since previous coupon payment
`daysInCouponPeriod`	days in a coupon period
`accruedInterest`	accrued interest since last coupon payment
`invoicePrice`	invoice price (= flat price + accrued interest)

Note

With Excel function YIELD you can do the same.

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Bond Pricing between Coupon Dates in Section 14.2).

Examples

solveYield("2012-7-31","2018-7-31",0.0225,100,2)
solveYield("2012-7-31","2018-7-31",0.0225,100,2)

Computing stock prices

Description

This function computes the intrinsic stock price using the constant growth dividend discount model.

Usage

stock.price(dividend, k = NULL, g = NULL, ROE = NULL, b = NULL, 
  riskFree = NULL, marketPremium = NULL, beta = NULL)
stock.price(dividend, k = NULL, g = NULL, ROE = NULL, b = NULL, 
  riskFree = NULL, marketPremium = NULL, beta = NULL)

Arguments

`dividend`	expected dividend(s) for the next year(s) (in euros), separated by commas
`k`	required rate of return
`g`	growth rate of dividends
`ROE`	return on investment
`b`	plowback ratio
`riskFree`	riskfree rate
`marketPremium`	market risk premium
`beta`	beta

Details

All the above rates are given in percentages (except the dividends). One should provide either k or the following three: riskFree, marketPremium, beta. Further, one should provide either g or the following two: ROE and b. In the output, k and g are given in decimals.

Value

`dividend`	expected dividend(s) for the next year(s) (in euros)
`k`	required rate of return
`g`	growth rate of dividends
`PVGO`	present value of growths opportunities
`stockPrice`	intrinsic stock price

Author(s)

Arto Luoma <[email protected]>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Dividend Discount Models in Section 18.3).

Examples

  stock.price(dividend=c(1),k=12,g=10)
  stock.price(dividend=c(1),ROE=50,b=20,riskFree=5,marketPremium=8,
              beta=90)
stock.price(dividend=c(1),k=12,g=10)
  stock.price(dividend=c(1),ROE=50,b=20,riskFree=5,marketPremium=8,
              beta=90)

Stock data

Description

Stock data on large companies in Helsinki Stock Exchange, downloaded from Kauppalehti web page (www.kauppalehti.fi), on May 13, 2017

Usage

data("stockData")data("stockData")

Format

A data frame with 35 observations on the following 7 variables.

names: name of the firm
abbrs: abbreviation of the firm
quote: closing quote
vol: volatility (%)
beta: beta (%)
div: dividend (eur/stock)
divYield: dividend yield (%)

Source

www.kauppalehti.fi

Examples

data(stockData)
plot(stockData[,-(1:2)])
data(stockData)
plot(stockData[,-(1:2)])

Package 'RcmdrPlugin.RiskDemo'

Help Index

R Commander Plug-in for Risk Demonstration

Description

Details

Author(s)

Drawing forward and yield curves

Description

Usage

Arguments

Value

Author(s)

References

Examples

Bond price as a function of interest rate.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Computing bond prices

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Ruin probability computation with infinite time horizon

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Ruin probability computation with finite time horizon

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Mortality data

Description

Usage

Format

Source

Examples

Kalman smoothing of the covid model

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

COVID-19 statistics

Description

Usage

Format

Details

Source

Examples

Confirmed COVID-19 cases in Finland

Description

Usage

Format

Details

Source