A Randomly Generated Pool of Variable Annuities

Description

A dataset containing information of the policy and the policy holder.

Usage

VAPort

Format

A data frame with 19 row and 45 columns:

recordID

Unique identifier of the policy

survivorShip

Positive weighting number

gender

Gender of the policyholder

productType

Product type

issueDate

Issue date

matDate

Maturity date

birthDate

Birth date of the policyholder

currentDate

Current date

baseFee

M&E (Mortality & Expense) fee

riderFee

Rider fee

rollUpRate

Roll-up rate

gbAmt

Guaranteed benefit

gmwbBalance

GMWB balance

wbWithdrawalRate

Guaranteed withdrawal rate

withdrawal

Withdrawal so far

fundNum1

Fund number of the 1st investment fund

fundNum2

Fund number of the 2nd investment fund

fundNum3

Fund number of the 3rd investment fund

fundNum4

Fund number of the 4th investment fund

fundNum5

Fund number of the 5th investment fund

fundNum6

Fund number of the 6th investment fund

fundNum7

Fund number of the 7th investment fund

fundNum8

Fund number of the 8th investment fund

fundNum9

Fund number of the 9th investment fund

fundNum10

Fund number of the 10th investment fund

fundValue1

Fund value of the 1st investment fund

fundValue2

Fund value of the 2nd investment fund

fundValue3

Fund value of the 3rd investment fund

fundValue4

Fund value of the 4th investment fund

fundValue5

Fund value of the 5th investment fund

fundValue6

Fund value of the 6th investment fund

fundValue7

Fund value of the 7th investment fund

fundValue8

Fund value of the 8th investment fund

fundValue9

Fund value of the 9th investment fund

fundValue10

Fund value of the 10th investment fund

fundFee1

Fund management fee of the 1st investment fund

fundFee2

Fund management fee of the 2nd investment fund

fundFee3

Fund management fee of the 3rd investment fund

fundFee4

Fund management fee of the 4th investment fund

fundFee5

Fund management fee of the 5th investment fund

fundFee6

Fund management fee of the 6th investment fund

fundFee7

Fund management fee of the 7th investment fund

fundFee8

Fund management fee of the 8th investment fund

fundFee9

Fund management fee of the 9th investment fund

fundFee10

Fund management fee of the 10th investment fund

...

Age One Policy

Description

Age a VA policy specified in inPolicy from currentDate (specified in inPolicy) to targetDate. The againg scenario is given in fundScen. The time step length is specified in dT. Here we input a rather irrelevant parameter df to "hack" for a more flexible user-defined projection function.

Usage

ageOnePolicy(
  inPolicy,
  mortTable,
  fundScen,
  scenDates,
  dT = 1/12,
  targetDate,
  df
)

Arguments

Value

Outputs a vector containing 45 attributes of a VA policy, where currentDate, gbAmt, GMWBbalance, withdrawal, & fundValue could be updated as a result of aging. Usually a row of a VA portfolio dataframe.

Note

Target date MUST be PRIOR to the last date of historical scenario date, Current date MUST be LATER than the first date of historical scenario date.

Examples

exPolicy <- VAPort[1, ]
targetDate <- "2016-01-01"
histFundScen <- genFundScen(fundMap, histIdxScen)
ageOnePolicy(exPolicy, mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)
## Not run: 
targetDate <- "2001-01-01"
histFundScen <- genFundScen(fundMap, histIdxScen)
ageOnePolicy(exPolicy, mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)

## End(Not run)
## Not run: 
exPolicy <- VAPort[1, ]
exPolicy[1, c("currentDate", "issueDate")] <- c("2001-01-01", "2001-01-01")
histFundScen <- genFundScen(fundMap, histIdxScen)
ageOnePolicy(exPolicy, mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)

## End(Not run)

Age a Portfolio

Description

Age a portfolio of VA policies specified in each inPolicy of inPortfolio from currentDate (specified in inPolicy) to targetDate. The againg scenario is given in fundScen. The time step length is specified in dT. Here we input a rather irrelevant parameter df to "hack" for a more flexible user-defined projection function.

Usage

agePortfolio(
  inPortfolio,
  mortTable,
  fundScen,
  scenDates,
  dT = 1/12,
  targetDate,
  df
)

Arguments

Value

Outputs a dataframe containing numPolicy rows and 45 attributes of each VA policy, where currentDate, gbAmt, GMWBbalance, withdrawal, & fundValue of each policy could be updated as a result of aging.

Note

Target date MUST be PRIOR to the last date of historical scenario date, Current date MUST be LATER than the first date of historical scenario date.

Examples

targetDate <- "2016-01-01"
histFundScen <- genFundScen(fundMap, histIdxScen)
agePortfolio(VAPort[1:2, ], mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)
## Not run: 
targetDate <- "2001-01-01"
histFundScen <- genFundScen(fundMap, histIdxScen)
agePortfolio(VAPort, mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)

## End(Not run)
## Not run: 
VAPort[1, c("currentDate", "issueDate")] <- c("2001-01-01", "2001-01-01")
histFundScen <- genFundScen(fundMap, histIdxScen)
agePortfolio(VAPort, mortTable, histFundScen, histDates, dT = 1 / 12,
targetDate, cForwardCurve)

## End(Not run)

Build Curve

Description

Bootstrap discount factors from a yield curve.

Usage

buildCurve(
  swapRates,
  tenors,
  fixFreq = 6,
  fixDCC = "Thirty360",
  fltFreq = 6,
  fltDCC = "Thirty360",
  calendar = "General",
  bdc = c("Actual", "Preceding", "Following", "Modified_Prec", "Modified_Foll"),
  curveDate,
  numSetDay,
  yieldCurveDCC = "Thirty360",
  holidays = NULL
)

Arguments

Value

Outputs a data frame of strings of discount dates and doubles of discount factors.

Examples

rate <- c(0.69, 0.77, 0.88, 1.01, 1.14, 1.38, 1.66, 2.15) * 0.01
tenor <- c(1, 2, 3, 4, 5, 7, 10, 30)
fixFreq <- 6
fixDCC <- "Thirty360"
fltFreq <- 6
fltDCC <- "ACT360"
calendar <- "NY"
bdc <- "Modified_Foll"
curveDate <- "2016-02-08"
numSetDay <- 2
yieldCurveDCC <- "Thirty360"
holidays <- NULL
buildCurve(rate, tenor, fixFreq, fixDCC, fltFreq, fltDCC, calendar, bdc,
           curveDate, numSetDay, yieldCurveDCC, holidays)

Constant Forward Curve

Description

A dataset containing 2 percent continuously compounded annual interest rate for illustration purposes.

Usage

cForwardCurve

Format

A vector with 360 elements:

rate

discount rate

...

Calculate Mortality Factors

Description

Calculates the mortality factors (t - 1)px q(x + t - 1) and tpx required to valuate the inPolicy. Extract gender, age (birth date & current date), valuation date (current date), and maturity date from inPolicy, mortality rates from mortTable.

Usage

calcMortFactors(inPolicy, mortTable, dT = 1/12)

Arguments

Value

Outputs a two-column data frame of doubles of mortFactors (t - 1)px q(x + t - 1) and tpx.

Examples

exPolicy <- VAPort[1, ]
calcMortFactors(exPolicy, mortTable, dT = 1 / 12)

Fund Map for 10 Funds

Description

A dataset containing a default mapping from five indices to ten different funds.

Usage

fundMap

Format

A matrix with 10 rows and 5 columns:

index name

name for each index

fund number

proportion of fund allocated to a particular index

...

Generate Fund Scenerio

Description

Calculate numScen-by-numStep-by-numFund fund scenarios based on given index scenarios indexScen and fund map fundMap that maps indices to funds.

Usage

genFundScen(fundMap, indexScen)

Arguments

Value

Outputs a numScen-by-numStep-by-numFund array of doubles of fund scenarios.

Examples

genFundScen(fundMap, indexScen)

Generate Index Scenerio

Description

Simulate a 3D array, numScen-by-numStep-by-numIndex, of Black-Scholes return factors for numIndex indices in each of numStep time steps and each of numScen scenarios. Covariances among indices are specified in covMatrix. Stepsize is given is dT and interpolated discount factors are given in vDF. Random seed is optional for reproducibility.

Usage

genIndexScen(
  covMatrix,
  numScen,
  numStep,
  indexNames,
  dT = 1/12,
  forwardCurve,
  seed
)

Arguments

Value

Outputs a 3D array (numScen-by-numStep-by-numIndex) of index scenarios

Examples

genIndexScen(mCov, 100, 360, indexNames, 1 / 12, cForwardCurve, 1)

Generate Portfolio at Inception

Description

Generate a portfolio of VA contracts at inception based on given attribute ranges and investment fund information.

Usage

genPortInception(
  birthDayRng = c("1950-01-01", "1980-01-01"),
  issueRng = c("2001-08-01", "2014-01-01"),
  matRng = c(15, 30),
  acctValueRng = c(50000, 5e+05),
  femPct = 0.4,
  fundFee = c(30, 50, 60, 80, 10, 38, 45, 55, 47, 46),
  baseFee = 200,
  prodPct = rep(1/19, 19),
  prodType = c("DBRP", "DBRU", "DBSU", "ABRP", "ABRU", "ABSU", "IBRP", "IBRU", "IBSU",
    "MBRP", "MBRU", "MBSU", "WBRP", "WBRU", "WBSU", "DBAB", "DBIB", "DBMB", "DBWB"),
  riderFee = c(25, 35, 35, 50, 60, 60, 60, 70, 70, 50, 60, 60, 65, 75, 75, 75, 85, 75,
    90),
  rollUpRate = rep(5, 19),
  withdrawalRate = rep(5, 19),
  numPolicy = 10
)

Arguments

Value

Outputs a data frame of 45 columns of attributes in an annuity contract.

Examples

genPortInception(c("1980-01-01", "1990-01-01"), c("2001-08-01", "2014-01-01"),
c(15, 30), c(5e4, 5e5), 0.4, c(30, 50, 60, 80, 10, 38, 45, 55, 47, 46),
200, rep(1 / 4, 4), c("WBRP", "WBRU", "WBSU", "DBWB"),
riderFee = c(25, 35, 35, 50), rep(5, 4), rep(5, 4), 100)
## Not run: 
genPortInception()

## End(Not run)

Historical Scenario Dates

Description

A dataset containing the dates at which historical returns for different indices were observed.

Usage

histDates

Format

A vector with 175 elements:

date

each observation date of the historical scenarios

...

Historical Index Scenario for 5 Indices over 175 Months

Description

A dataset containing a matrix, number of indices (5) by number of time steps (175), of observed historical returns for each index in each of time step in the past.

Usage

histIdxScen

Format

A data frame with dimensions 175 rows and 10 columns:

FIXED

historical return for index "FIXED" in one month

INT

historical return for index "INT" in one month

MONEY

historical return for index "MONEY" in one month

SMALL

historical return for index "SMALL" in one month

US

historical return for index "US" in one month

...

Remark

These historical index scenarios were assessed on 2008-09-12

Source

http://www.math.uconn.edu/~gan/software.html

Index Names

Description

A dataset containing names for each index.

Usage

indexNames

Format

A vector with 5 elements:

name

name of the index

...

5 Indices for 10 Scenarios over 360 Months

Description

A dataset containing a 3D array, number of scenarios (10) by number of indices (5) by number of time steps (360), of Black-Scholes return factors for each index in each of time step and each of scenario.

Usage

indexScen

Format

A 3D array with dimensions 10x360x5:

scenario

scenario number

month

month since valuation date

index number

monthly return for a particular index in one scenario one month

...

Covariance Matrix for 5 Indices

Description

A dataset containing the covariance matrix among the returns of five indices.

Usage

mCov

Format

A matrix with 5 rows and 5 columns:

index number

number for each index

...

Mortality Rate for Male and Female from Ages 5 to 115

Description

A dataset containing the mortality rates for male and female from ages 5 to 115 (table IAM 1996 from the Society of Actuaries).

Usage

mortTable

Format

A data frame with 110 rows and 3 columns:

age

individual's age

male

mortality of a male at a particular age ranging from 5 to 115

female

mortality of a female at a particular age ranging from 5 to 115

...

Source

https://mort.soa.org

Swap Rates across 30 Years

Description

A dataset containing US swap rates for various maturities.

Usage

swapRate

Format

A vector with 8 elements:

rate

swap rate

...

Remark

These swap rates were assessed on 2016-02-08

Source

http://www.federalreserve.gov

Valuate One Policy

Description

Valuate a VA policy specified in inPolicy based on the simulated fund scenarios fundScen. The time step length is specified in dT and the discount rate for each period is specified in df.

Usage

valuateOnePolicy(inPolicy, mortTable, fundScen, dT = 1/12, df)

Arguments

Value

Outputs a list of doubles of policyValue, the average discounted payoff of the VA, and riskCharge, the average discounted risk charges.

Examples

fundScen <- genFundScen(fundMap, indexScen)[1, , ]
exPolicy <- VAPort[1, ]
valuateOnePolicy(exPolicy, mortTable, fundScen, 1 / 12, cForwardCurve)

Valuate a Portfolio

Description

Valuate a portfolio VA policies specified in each curPolicy of inPortfolio based on the simulated fund scenarios fundScen. The time step length is specified in dT and the discount rate for each period is specified in df.

Usage

valuatePortfolio(inPortfolio, mortTable, fundScen, dT = 1/12, df)

Arguments

Value

Outputs a list of doubles of portVal, the sum of average discounted payoff of the VAs in inPortfolio, portRC, the sum of average discounted risk charges of the VAs in inPortfolio, and vectors of doubles of these average discounted values for each policy.

Examples

fundScen <- genFundScen(fundMap, indexScen)[1, , ]
valuatePortfolio(VAPort[1:2, ], mortTable, fundScen, 1 / 12, cForwardCurve)

vamc: A package for pricing a pool of variable annuities.

Description

The vamc package provides a Monte Carlo engine for valuating a pool of variable annuities. The key steps are: YieldCurveGeneration, ScenarioGeneration, PolicyGenerationl, and MonteCarloValuation.

YieldCurveGeneration functions

YieldCurveGeneration generates a forward curve from swap rates. The forward curve is obtained by solving for swap rates that equates values of floating and fixed notes.

ScenarioGeneration functions

ScenarioGeneration generates a random fund scenario under Black-Scholes. After simulating random index scenarios, a fundMap is used to allocate returns of indices to each fund according to proportion of investment.

PolicyGenerationl functions

PolicyGenerationl randomly generates a pool of variable annuities for user-input birthday range, issue-date range, maturity range, account value range, female percentage, fund management fee, fund base fee, product types, rider fee of each type, roll-up-rate for roll-up featured guarantees, withdrawal rate for GMWB, and number of policies to be generated for each type.

MonteCarloValuation functions

MonteCarloValuation discounts cash flow from living and death benefits, as well as risk charges for each policy in the portfolio.

References

Gan G, Valdez EA (2017). “Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets.” Dependence Modeling, 5, 354–374. doi: 10.1515/demo-2017-0021.